Solution of the pulse width modulation problem using orthogonal polynomials and Korteweg-de Vries equations

The mathematical underpinning of the pulse width modulation (PWM) technique lies in the attempt to represent “accurately” harmonic waveforms using only square forms of a fixed height. The accuracy can be measured using many norms, but the quality of the approximation of the analog signal (a harmonic form) by a digital one (simple pulses of a fixed high voltage level) requires the elimination of high order harmonics in the error term. The most important practical problem is in “accurate” reproduction of sine-wave using the same number of pulses as the number of high harmonics eliminated. We describe in this paper a complete solution of the PWM problem using Padé approximations, orthogonal polynomials, and solitons. The main result of the paper is the characterization of discrete pulses answering the general PWM problem in terms of the manifold of all rational solutions to Korteweg-de Vries equations.

Catalogus van eene fraaije verzameling kapitale origineele Engelsche en andere gekleurde en ongekleurde prenten, in vergulde lijsten, met geamailleerde glazen, als mede eene verzameling fraaije teekeningen, voorts ... gebonden en losse prent- en boekwerken ... alles te zamen uitmakende het gerenomeerd kunstmagazijn van den heere C. Josi : hetwelk verkocht zal worden op Maandag, den 20sten April 1818, ten huize van C. Roos, in het "Huis met de Hoofden", op de Keizersgracht, bij de Leliegracht, te Amsterdam, door de makelaars: Cornelis Sebille Roos, Jeronimo de Vries en Albertus Brondgeest : de catalogus is tegens betaling van 51/2 stuiver te bekomen ....

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Les invariants de la chaleur en dimensions 1 et 2, et application à la hiérarchie de Korteweg-De Vries

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Les invariants de la chaleur en dimensions 1 et 2, et application à la hiérarchie de Korteweg-De Vries

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

K-tree : large scale document clustering

We introduce K-tree in an information retrieval context. It is an efficient approximation of the k-means clustering algorithm. Unlike k-means it forms a hierarchy of clusters. It has been extended to address issues with sparse representations. We compare performance and quality to CLUTO using document collections. The K-tree has a low time complexity that is suitable for large document collections. This tree structure allows for efficient disk based implementations where space requirements exceed that of main memory.

Document clustering with K-tree

This paper describes the approach taken to the XML Mining track at INEX 2008 by a group at the Queensland University of Technology. We introduce the K-tree clustering algorithm in an Information Retrieval context by adapting it for document clustering. Many large scale problems exist in document clustering. K-tree scales well with large inputs due to its low complexity. It offers promising results both in terms of efficiency and quality. Document classification was completed using Support Vector Machines.

Random Indexing K-tree

Random Indexing K-tree is the combination of two algorithms suited for large scale document clustering.

Clustering with random indexing K-tree and XML structure

This paper describes the approach taken to the clustering task at INEX 2009 by a group at the Queensland University of Technology. The Random Indexing (RI) K-tree has been used with a representation that is based on the semantic markup available in the INEX 2009 Wikipedia collection. The RI K-tree is a scalable approach to clustering large document collections. This approach has produced quality clustering when evaluated using two different methodologies.

Overview of the INEX 2009 XML mining track : clustering and classification of XML documents

This report explains the objectives, datasets and evaluation criteria of both the clustering and classification tasks set in the INEX 2009 XML Mining track. The report also describes the approaches and results obtained by the different participants.

Application of K-tree to document clustering

Digital collections are growing exponentially in size as the information age takes a firm grip on all aspects of society. As a result Information Retrieval (IR) has become an increasingly important area of research. It promises to provide new and more effective ways for users to find information relevant to their search intentions. Document clustering is one of the many tools in the IR toolbox and is far from being perfected. It groups documents that share common features. This grouping allows a user to quickly identify relevant information. If these groups are misleading then valuable information can accidentally be ignored. There- fore, the study and analysis of the quality of document clustering is important. With more and more digital information available, the performance of these algorithms is also of interest. An algorithm with a time complexity of O(n2) can quickly become impractical when clustering a corpus containing millions of documents. Therefore, the investigation of algorithms and data structures to perform clustering in an efficient manner is vital to its success as an IR tool. Document classification is another tool frequently used in the IR field. It predicts categories of new documents based on an existing database of (doc- ument, category) pairs. Support Vector Machines (SVM) have been found to be effective when classifying text documents. As the algorithms for classifica- tion are both efficient and of high quality, the largest gains can be made from improvements to representation. Document representations are vital for both clustering and classification. Representations exploit the content and structure of documents. Dimensionality reduction can improve the effectiveness of existing representations in terms of quality and run-time performance. Research into these areas is another way to improve the efficiency and quality of clustering and classification results. Evaluating document clustering is a difficult task. Intrinsic measures of quality such as distortion only indicate how well an algorithm minimised a sim- ilarity function in a particular vector space. Intrinsic comparisons are inherently limited by the given representation and are not comparable between different representations. Extrinsic measures of quality compare a clustering solution to a “ground truth” solution. This allows comparison between different approaches. As the “ground truth” is created by humans it can suffer from the fact that not every human interprets a topic in the same manner. Whether a document belongs to a particular topic or not can be subjective.

Deliberative assessment of surrogate consent in dementia research

Background Research involving incapacitated persons with dementia entails complex scientific, legal, and ethical issues, making traditional surveys of layperson views on the ethics of such research challenging. We therefore assessed the impact of democratic deliberation (DD), involving balanced, detailed education and peer deliberation, on the views of those responsible for persons with dementia. Methods One hundred and seventy-eight community-recruited caregivers or primary decision-makers for persons with dementia were randomly assigned to either an all-day DD session group or a control group. Educational materials used for the DD session were vetted for balance and accuracy by an interdisciplinary advisory panel. We assessed the acceptability of family-surrogate consent for dementia research (“surrogate-based research”) from a societal policy perspective as well as from the more personal perspectives of deciding for a loved one or for oneself (surrogate and self-perspectives), assessed at baseline, immediately post-DD session, and 1 month after DD date, for four research scenarios of varying risk-benefit profiles. Results At baseline, a majority in both the DD and control groups supported a policy of family consent for dementia research in all research scenarios. The support for a policy of family consent for surrogate-based research increased in the DD group, but not in the control group. The change in the DD group was maintained 1 month later. In the DD group, there were transient changes in attitudes from surrogate or self-perspectives. In the control group, there were no changes from baseline in attitude toward surrogate consent from any perspective. Conclusions Intensive, balanced, and accurate education, along with peer deliberation provided by democratic deliberation, led to a sustained increase in support for a societal policy of family consent in dementia research among those responsible for dementia patients.

Overview of the INEX 2010 XML mining track : clustering and classification of XML documents

The XML Document Mining track was launched for exploring two main ideas: (1) identifying key problems and new challenges of the emerging field of mining semi-structured documents, and (2) studying and assessing the potential of Machine Learning (ML) techniques for dealing with generic ML tasks in the structured domain, i.e., classification and clustering of semi-structured documents. This track has run for six editions during INEX 2005, 2006, 2007, 2008, 2009 and 2010. The first five editions have been summarized in previous editions and we focus here on the 2010 edition. INEX 2010 included two tasks in the XML Mining track: (1) unsupervised clustering task and (2) semi-supervised classification task where documents are organized in a graph. The clustering task requires the participants to group the documents into clusters without any knowledge of category labels using an unsupervised learning algorithm. On the other hand, the classification task requires the participants to label the documents in the dataset into known categories using a supervised learning algorithm and a training set. This report gives the details of clustering and classification tasks.

Pyktree : a K-tree implementation in Python

In this paper we present pyktree, an implementation of the K-tree algorithm in the Python programming language. The K-tree algorithm provides highly balanced search trees for vector quantization that scales up to very large data sets. Pyktree is highly modular and well suited for rapid-prototyping of novel distance measures and centroid representations. It is easy to install and provides a python package for library use as well as command line tools.