4,255 research outputs found
Median evidential c-means algorithm and its application to community detection
Median clustering is of great value for partitioning relational data. In this
paper, a new prototype-based clustering method, called Median Evidential
C-Means (MECM), which is an extension of median c-means and median fuzzy
c-means on the theoretical framework of belief functions is proposed. The
median variant relaxes the restriction of a metric space embedding for the
objects but constrains the prototypes to be in the original data set. Due to
these properties, MECM could be applied to graph clustering problems. A
community detection scheme for social networks based on MECM is investigated
and the obtained credal partitions of graphs, which are more refined than crisp
and fuzzy ones, enable us to have a better understanding of the graph
structures. An initial prototype-selection scheme based on evidential
semi-centrality is presented to avoid local premature convergence and an
evidential modularity function is defined to choose the optimal number of
communities. Finally, experiments in synthetic and real data sets illustrate
the performance of MECM and show its difference to other methods
Finding Periodic Apartments : A Computational Study of Hyperbolic Buildings
This thesis presents a computational study of a fundamental open conjecture in geometric group theory using an intricate combination of Boolean Satisfiability and orderly generation. In particular, we focus on Gromovâs subgroup conjecture (GSC), which states that âeach one-ended hyperbolic group contains a subgroup isomorphic to the fundamental group of a closed surface of genus at least 2â. Several classes of groups have been shown to satisfy GSC, but the status of non-right-angled groups with regard to GSC is presently unknown, and may provide counterexamples to the conjecture. With this in mind Kangaslampi and Vdovina constructed 23 such groups utilizing the theory of hyperbolic buildings [International Journal of Algebra and Computation, vol. 20, no. 4, pp. 591â603, 2010], and ran an exhaustive computational analysis of surface subgroups of genus 2 arising from so-called periodic apartments [Experimental Mathematics, vol. 26, no. 1, pp. 54â61, 2017]. While they were able to rule out 5 of the 23 groups as potential counterexamples to GSC, they reported that their computational approach does not scale to genera higher than 2. We extend the work of Kangaslampi and Vdovina by developing two new approaches to analyzing the subgroups arising from periodic apartments in the 23 groups utilizing different combinations of SAT solving and orderly generation. We develop novel SAT encodings and a specialized orderly algorithm for the approaches, and perform an exhaustive analysis (over the 23 groups) of the genus 3 subgroups arising from periodic apartments. With the aid of massively parallel computation we also exhaust the case of genus 4. As a result we rule out 4 additional groups as counterexamples to GSC leaving 14 of the 23 groups for further inspection. In addition to this our approach provides an independent verification of the genus 2 results reported by Kangaslampi and Vdovina
The Vadalog System: Datalog-based Reasoning for Knowledge Graphs
Over the past years, there has been a resurgence of Datalog-based systems in
the database community as well as in industry. In this context, it has been
recognized that to handle the complex knowl\-edge-based scenarios encountered
today, such as reasoning over large knowledge graphs, Datalog has to be
extended with features such as existential quantification. Yet, Datalog-based
reasoning in the presence of existential quantification is in general
undecidable. Many efforts have been made to define decidable fragments. Warded
Datalog+/- is a very promising one, as it captures PTIME complexity while
allowing ontological reasoning. Yet so far, no implementation of Warded
Datalog+/- was available. In this paper we present the Vadalog system, a
Datalog-based system for performing complex logic reasoning tasks, such as
those required in advanced knowledge graphs. The Vadalog system is Oxford's
contribution to the VADA research programme, a joint effort of the universities
of Oxford, Manchester and Edinburgh and around 20 industrial partners. As the
main contribution of this paper, we illustrate the first implementation of
Warded Datalog+/-, a high-performance Datalog+/- system utilizing an aggressive
termination control strategy. We also provide a comprehensive experimental
evaluation.Comment: Extended version of VLDB paper
<https://doi.org/10.14778/3213880.3213888
An adaptive prefix-assignment technique for symmetry reduction
This paper presents a technique for symmetry reduction that adaptively
assigns a prefix of variables in a system of constraints so that the generated
prefix-assignments are pairwise nonisomorphic under the action of the symmetry
group of the system. The technique is based on McKay's canonical extension
framework [J.~Algorithms 26 (1998), no.~2, 306--324]. Among key features of the
technique are (i) adaptability---the prefix sequence can be user-prescribed and
truncated for compatibility with the group of symmetries; (ii)
parallelizability---prefix-assignments can be processed in parallel
independently of each other; (iii) versatility---the method is applicable
whenever the group of symmetries can be concisely represented as the
automorphism group of a vertex-colored graph; and (iv) implementability---the
method can be implemented relying on a canonical labeling map for
vertex-colored graphs as the only nontrivial subroutine. To demonstrate the
practical applicability of our technique, we have prepared an experimental
open-source implementation of the technique and carry out a set of experiments
that demonstrate ability to reduce symmetry on hard instances. Furthermore, we
demonstrate that the implementation effectively parallelizes to compute
clusters with multiple nodes via a message-passing interface.Comment: Updated manuscript submitted for revie
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Enumerating molecules.
This report is a comprehensive review of the field of molecular enumeration from early isomer counting theories to evolutionary algorithms that design molecules in silico. The core of the review is a detail account on how molecules are counted, enumerated, and sampled. The practical applications of molecular enumeration are also reviewed for chemical information, structure elucidation, molecular design, and combinatorial library design purposes. This review is to appear as a chapter in Reviews in Computational Chemistry volume 21 edited by Kenny B. Lipkowitz
ĂlĆlĂ©nyek kollektĂv viselkedĂ©sĂ©nek statisztikus fizikĂĄja = Statistical physics of the collective behaviour of organisms
Experiments: We have carried out quantitative experiments on the collective motion of cells as a function of their density. A sharp transition could be observed from the random motility in sparse cultures to the flocking of dense islands of cells. Using ultra light GPS devices developed by us, we have determined the existing hierarchical relations within a flock of 10 homing pigeons. Modelling: From the simulations of our new model of flocking we concluded that the information exchange between particles was maximal at the critical point, in which the interplay of such factors as the level of noise, the tendency to follow the direction and the acceleration of others results in large fluctuations. Analysis: We have proposed a novel link-density based approach to finding overlapping communities in large networks. The algorithm used for the implementation of this technique is very efficient for most real networks, and provides full statistics quickly. Correspondingly, we have developed a by now popular, user-friendly, freely downloadable software for finding overlapping communities. Extending our method to the time-dependent regime, we found that large groups in evolving networks persist for longer if they are capable of dynamically altering their membership, thus, an ability to change the group composition results in better adaptability. We also showed that knowledge of the time commitment of members to a given community can be used for estimating the community's lifetime. Experiments: We have carried out quantitative experiments on the collective motion of cells as a function of their density. A sharp transition could be observed from the random motility in sparse cultures to the flocking of dense islands of cells. Using ultra light GPS devices developed by us, we have determined the existing hierarchical relations within a flock of 10 homing pigeons. Modelling: From the simulations of our new model of flocking we concluded that the information exchange between particles was maximal at the critical point, in which the interplay of such factors as the level of noise, the tendency to follow the direction and the acceleration of others results in large fluctuations. Analysis: We have proposed a novel link-density based approach to finding overlapping communities in large networks. The algorithm used for the implementation of this technique is very efficient for most real networks, and provides full statistics quickly. Correspondingly, we have developed a by now popular, user-friendly, freely downloadable software for finding overlapping communities. Extending our method to the time-dependent regime, we found that large groups in evolving networks persist for longer if they are capable of dynamically altering their membership, thus, an ability to change the group composition results in better adaptability. We also showed that knowledge of the time commitment of members to a given community can be used for estimating the community's lifetime
Uniform random sampling of planar graphs in linear time
This article introduces new algorithms for the uniform random generation of
labelled planar graphs. Its principles rely on Boltzmann samplers, as recently
developed by Duchon, Flajolet, Louchard, and Schaeffer. It combines the
Boltzmann framework, a suitable use of rejection, a new combinatorial bijection
found by Fusy, Poulalhon and Schaeffer, as well as a precise analytic
description of the generating functions counting planar graphs, which was
recently obtained by Gim\'enez and Noy. This gives rise to an extremely
efficient algorithm for the random generation of planar graphs. There is a
preprocessing step of some fixed small cost. Then, the expected time complexity
of generation is quadratic for exact-size uniform sampling and linear for
approximate-size sampling. This greatly improves on the best previously known
time complexity for exact-size uniform sampling of planar graphs with
vertices, which was a little over .Comment: 55 page
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