Margareta Ackerman

Efficient enumeration of words in regular languages

The cross-section enumeration problem is to list all words of length n in a regular language L in lexicographical order. The enumeration problem is to list the first m words in L according to radix order. We present an algorithm for the cross-section enumeration problem that is linear in n+t, where t is the output size. We provide a detailed analysis of the asymptotic running time of our algorithm and that of known algorithms for both enumeration problems. We discuss some shortcomings of the enumeration algorithm found in the Grail computation package. In the practical domain, we modify Makinens enumeration algorithm to get an algorithm that is usually the most efficient in practice. We performed an extensive performance analysis of the new and previously known enumeration and cross-section enumeration algorithms and found when each algorithm is preferable.

Efficient enumeration of regular languages

The cross-section enumeration problem is to list all words of length n in a regular language L in lexicographical order. The enumeration problem is to list the first m words in L according to radix order. We present an algorithm for the cross-section enumeration problem that is linear in n. We provide a detailed analysis of the asymptotic running time of our algorithm and that of known algorithms for both enumeration problems. We discuss some shortcomings of the enumeration algorithm found in the Grail computation package. In the practical domain, we modify Makinens enumeration algorithm to get an algorithm that is usually the most efficient in practice. We performed an extensive performance analysis of the new and previously known enumeration and cross-section enumeration algorithms and found when each algorithm is preferable.

Three New Algorithms for Regular Language Enumeration

We present new and more efficient algorithms for regular language enumeration problems. The min-word problem is to find the lexicographically minimal word of length n accepted by a given NFA, the cross-section problem is to list all words of length n accepted by an NFA in lexicographical order, and the enumeration problem is to list the first m words accepted by an NFA according to length-lexicographic order. For the min-word and cross-section problems, we present algorithms with better asymptotic running times than previously known algorithms. Additionally, for each problem, we present algorithms with better practical running times than previously known algorithms.

The authorship dilemma: alphabetical or contribution?

Scientific communities have adopted different conventions for ordering authors on publications. Are these choices inconsequential, or do they have significant influence on individual authors, the quality of the projects completed, and research communities at large? What are the trade-offs of using one convention over another? In order to investigate these questions, we formulate a basic two-player game theoretic model, which already illustrates interesting phenomena that can occur in more realistic settings. We find that contribution-based ordering leads to a denser collaboration network and a greater number of publications, while alphabetical ordering can improve research quality. Contrary to the assumption that free riding is a weakness of the alphabetical ordering scheme, when there are only two authors, this phenomenon can occur under any contribution scheme, and the worst case occurs under contribution-based ordering. Finally, we show how authors working on multiple projects can cooperate to attain optimal research quality and eliminate free riding given either contribution scheme.

Algorithmic Songwriting with ALYSIA

This paper introduces ALYSIA: Automated LYrical SongwrIting Application. ALYSIA is based on a machine learning model using Random Forests, and we discuss its success at pitch and rhythm prediction. Next, we show how ALYSIA was used to create original pop songs that were subsequently recorded and produced. Finally, we discuss our vision for the future of Automated Songwriting for both co-creative and autonomous systems.

To Cluster, or Not to Cluster: An Analysis of Clusterability Methods

Abstract Clustering is an essential data mining tool that aims to discover inherent cluster structure in data. For most applications, applying clustering is only appropriate when cluster structure is present. As such, the study of clusterability, which evaluates whether data possesses such structure, is an integral part of cluster analysis. However, methods for evaluating clusterability vary radically, making it challenging to select a suitable measure. In this paper, we perform an extensive comparison of measures of clusterability and provide guidelines that clustering users can reference to select suitable measures for their applications.

Foundations of Perturbation Robust Clustering

Clustering is a fundamental data mining tool that aims to divide data into groups of similar items. Intuition about clustering reflects the ideal case – exact data sets endowed with flawless dissimilarity between individual instances. In practice however, these cases are in the minority, and clustering applications are typically characterized by noisy data sets with approximate pairwise dissimilarities. As such, the efficacy of clustering methods necessitates robustness to perturbations. In this paper, we address foundational questions on perturbation robustness, studying to what extent can clustering techniques exhibit this desirable characteristic. Our results also demonstrate the type of cluster structures required for robustness of popular clustering paradigms.

Effects of rooting via out-groups on in-group topology in phylogeny

Users of phylogenetic methods require rooted trees, because the direction of time depends on the placement of the root. While phylogenetic trees are typically rooted by using an out-group, this mechanism is inappropriate when the addition of an out-group changes the in-group topology. We perform a formal analysis of phylogenetic algorithms under the inclusion of distant out-groups. It turns out that linkage-based algorithms (including UPGMA) and a class of bisecting methods do not modify the topology of the in-group when an out-group is included. By contrast, the popular neighbour joining algorithm fails this property in a strong sense: every data set can have its structure destroyed by some arbitrarily distant outlier. Furthermore, including multiple outliers can lead to an arbitrary topology on the in-group. The standard rooting approach that uses out-groups may be fundamentally unsuited for neighbour joining.

Effects of rooting via outgroups on ingroup topology in phylogeny

Users of phylogenetic methods require rooted trees, because the direction of time depends on the placement of the root. Phylogenetic trees are typically rooted through the use of an outgroup. However, this rooting mechanism is inappropriate when adding an outgroup yields a different topology for the ingroup. We perform a formal analysis of the response of different phylogenetic algorithms to the inclusion of distant outgroups. We prove that linkage-based algorithms, which include UP-GMA, do not modify the topology of the ingroup when an outgroup is included. A class of bisecting algorithms are similarly unaffected. These results are the first to provide formal guarantees on the use of outgroups for rooting phylogentic trees, guaranteeing that this rooting mechanism will not effect the structure of any ingroup when certain algorithms are used. By contrast, the popular neighbour joining algorithm fails this property in a strong sense. Every data set can have its structure destroyed by some arbitrarily distant outlier. Moreover, including multiple outliers can lead to an arbitrary topology on the ingroup. The standard rooting approach that uses outgroups may be fundamentally unsuited for neighbour joining.