626 research outputs found
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 % 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 -algebras, are finite
factorization domains (FFD for short).
Utilizing this result, we contribute an algorithm to find all distinct
factorizations of a given element , where is
any -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 -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
. 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. <br><br> 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. <br><br> 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
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