Fast Hierarchical Clustering and Other Applications of Dynamic Closest Pairs

We develop data structures for dynamic closest pair problems with arbitrary distance functions, that do not necessarily come from any geometric structure on the objects. Based on a technique previously used by the author for Euclidean closest pairs, we show how to insert and delete objects from an n-object set, maintaining the closest pair, in O(n log^2 n) time per update and O(n) space. With quadratic space, we can instead use a quadtree-like structure to achieve an optimal time bound, O(n) per update. We apply these data structures to hierarchical clustering, greedy matching, and TSP heuristics, and discuss other potential applications in machine learning, Groebner bases, and local improvement algorithms for partition and placement problems. Experiments show our new methods to be faster in practice than previously used heuristics.Comment: 20 pages, 9 figures. A preliminary version of this paper appeared at the 9th ACM-SIAM Symp. on Discrete Algorithms, San Francisco, 1998, pp. 619-628. For source code and experimental results, see http://www.ics.uci.edu/~eppstein/projects/pairs

Solving the 100 Swiss Francs Problem

Sturmfels offered 100 Swiss Francs in 2005 to a conjecture, which deals with a special case of the maximum likelihood estimation for a latent class model. This paper confirms the conjecture positively

Proof-Pattern Recognition and Lemma Discovery in ACL2

We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery. The resulting tool, ACL2(ml), gathers proof statistics and uses statistical pattern-recognition to pre-processes data from libraries, and then suggests auxiliary lemmas in new proofs by analogy with already seen examples. This paper presents the implementation of ACL2(ml) alongside theoretical descriptions of the proof-pattern recognition and lemma discovery methods involved in it

Growth Histories in Bimetric Massive Gravity

We perform cosmological perturbation theory in Hassan-Rosen bimetric gravity for general homogeneous and isotropic backgrounds. In the de Sitter approximation, we obtain decoupled sets of massless and massive scalar gravitational fluctuations. Matter perturbations then evolve like in Einstein gravity. We perturb the future de Sitter regime by the ratio of matter to dark energy, producing quasi-de Sitter space. In this more general setting the massive and massless fluctuations mix. We argue that in the quasi-de Sitter regime, the growth of structure in bimetric gravity differs from that of Einstein gravity.Comment: 28 pages + appendix, 11 figure

An Algorithm to Construct Groebner Bases for Solving Integration by Parts Relations

This paper is a detailed description of an algorithm based on a generalized Buchberger algorithm for constructing Groebner-type bases associated with polynomials of shift operators. The algorithm is used for calculating Feynman integrals and has proven itself efficient in several complicated cases.Comment: LaTeX, 9 page

Exploring the relationships between warm-season precipitation, potential evaporation, and “apparent” potential evaporation at site scale

Bouchet's complementary relationship and the Budyko hypothesis are two classic frameworks that are inter-connected. To systematically investigate the connections between the two frameworks, we analyze precipitation, pan evaporation, and potential evaporation data at 259 weather stations across the United States. The precipitation and pan evaporation data are from field measurement and the potential evaporation data are collected from a remote-sensing dataset. We use pan evaporation to represent apparent potential evaporation, which is different from potential evaporation. With these data, we study the correlations between precipitation and potential evaporation, and between precipitation and apparent potential evaporation. The results show that 93&thinsp;% of the study's weather stations exhibit a negative correlation between precipitation and apparent potential evaporation. Also, the aggregated data cloud of precipitation vs. apparent potential evaporation with 5312 warm-season data points from 259 weather stations shows a negative trend in which apparent potential evaporation decreases with increasing precipitation. On the other hand, no significant correlation is found in the data cloud of precipitation vs. potential evaporation, indicating that precipitation and potential evaporation are independent. We combine a Budyko-type expression, the Turc–Pike equation, with Bouchet's complementary relationship to derive upper and lower Bouchet–Budyko curves, which display a complementary relationship between apparent potential evaporation and actual evaporation. The observed warm-season data follow the trend of the Bouchet–Budyko curves. Our study shows the consistency between Budyko's framework and Bouchet's complementary relationship, with the distinction between potential evaporation and apparent potential evaporation. The formulated complementary relationship can be used in quantitative modeling practices.</p

CBR in Dependency-based Machine Translation

A case based reasoning approach is introduced as a learning technique in the domain of machine translation of natural language. In our approach syntactical and semantic features are part of the cases in the case-base. To implement this, dependency analysers of sentences in the source and target languages are used. The case-base is filled with a learning mechanism that uses a parallel corpus of sentences with their translations. This case-base is used to make new translations

A Factorization Algorithm for G-Algebras and Applications

It has been recently discovered by Bell, Heinle and Levandovskyy that a large class of algebras, including the ubiquitous $G$-algebras, are finite factorization domains (FFD for short). Utilizing this result, we contribute an algorithm to find all distinct factorizations of a given element $f \in \mathcal{G}$, where $\mathcal{G}$ is any $G$-algebra, with minor assumptions on the underlying field. Moreover, the property of being an FFD, in combination with the factorization algorithm, enables us to propose an analogous description of the factorized Gr\"obner basis algorithm for $G$-algebras. This algorithm is useful for various applications, e.g. in analysis of solution spaces of systems of linear partial functional equations with polynomial coefficients, coming from $\mathcal{G}$. Additionally, it is possible to include inequality constraints for ideals in the input

Importance of demand modelling in network water quality models: a review

Today, there is a growing interest in network water quality modelling. The water quality issues of interest relate to both dissolved and particulate substances. For dissolved substances the main interest is in residual chlorine and (microbiological) contaminant propagation; for particulate substances it is in sediment leading to discolouration. There is a strong influence of flows and velocities on transport, mixing, production and decay of these substances in the network. This imposes a different approach to demand modelling which is reviewed in this article. &lt;br&gt;&lt;br&gt; For the large diameter lines that comprise the transport portion of a typical municipal pipe system, a skeletonised network model with a top-down approach of demand pattern allocation, a hydraulic time step of 1 h, and a pure advection-reaction water quality model will usually suffice. For the smaller diameter lines that comprise the distribution portion of a municipal pipe system, an all-pipes network model with a bottom-up approach of demand pattern allocation, a hydraulic time step of 1 min or less, and a water quality model that considers dispersion and transients may be needed. &lt;br&gt;&lt;br&gt; Demand models that provide stochastic residential demands per individual home and on a one-second time scale are available. A stochastic demands based network water quality model needs to be developed and validated with field measurements. Such a model will be probabilistic in nature and will offer a new perspective for assessing water quality in the drinking water distribution system