41,533 research outputs found
Equivalent relaxations of optimal power flow
Several convex relaxations of the optimal power flow (OPF) problem have
recently been developed using both bus injection models and branch flow models.
In this paper, we prove relations among three convex relaxations: a
semidefinite relaxation that computes a full matrix, a chordal relaxation based
on a chordal extension of the network graph, and a second-order cone relaxation
that computes the smallest partial matrix. We prove a bijection between the
feasible sets of the OPF in the bus injection model and the branch flow model,
establishing the equivalence of these two models and their second-order cone
relaxations. Our results imply that, for radial networks, all these relaxations
are equivalent and one should always solve the second-order cone relaxation.
For mesh networks, the semidefinite relaxation is tighter than the second-order
cone relaxation but requires a heavier computational effort, and the chordal
relaxation strikes a good balance. Simulations are used to illustrate these
results.Comment: 12 pages, 7 figure
Finiteness theorems in stochastic integer programming
We study Graver test sets for families of linear multi-stage stochastic
integer programs with varying number of scenarios. We show that these test sets
can be decomposed into finitely many ``building blocks'', independent of the
number of scenarios, and we give an effective procedure to compute these
building blocks. The paper includes an introduction to Nash-Williams' theory of
better-quasi-orderings, which is used to show termination of our algorithm. We
also apply this theory to finiteness results for Hilbert functions.Comment: 36 p
Lifted rule injection for relation embeddings
Methods based on representation learning currently hold the state-of-the-art in many natural language processing and knowledge base inference tasks. Yet, a major challenge is how to efficiently incorporate commonsense knowledge into such models. A recent approach regularizes relation and entity representations by propositionalization of first-order logic rules. However, propositionalization does not scale beyond domains with only few entities and rules. In this paper we present a highly efficient method for incorporating implication rules into distributed representations for automated knowledge base construction. We map entity-tuple embeddings into an approximately Boolean space and encourage a partial ordering over relation embeddings based on implication rules mined from WordNet. Surprisingly, we find that the strong restriction of the entity-tuple embedding space does not hurt the expressiveness of the model and even acts as a regularizer that improves generalization. By incorporating few commonsense rules, we achieve an increase of 2 percentage points mean average precision over a matrix factorization baseline, while observing a negligible increase in runtime
12th International Workshop on Termination (WST 2012) : WST 2012, February 19â23, 2012, Obergurgl, Austria / ed. by Georg Moser
This volume contains the proceedings of the 12th International Workshop on Termination (WST 2012), to be held February 19â23, 2012 in Obergurgl, Austria. The goal of the Workshop on Termination is to be a venue for presentation and discussion of all topics in and around termination. In this way, the workshop tries to bridge the gaps between different communities interested and active in research in and around termination. The 12th International Workshop on Termination in Obergurgl continues the successful workshops held in St. Andrews (1993), La Bresse (1995), Ede (1997), Dagstuhl (1999), Utrecht (2001), Valencia (2003), Aachen (2004), Seattle (2006), Paris (2007), Leipzig (2009), and Edinburgh (2010). The 12th International Workshop on Termination did welcome contributions on all aspects of termination and complexity analysis. Contributions from the imperative, constraint, functional, and logic programming communities, and papers investigating applications of complexity or termination (for example in program transformation or theorem proving) were particularly welcome. We did receive 18 submissions which all were accepted. Each paper was assigned two reviewers. In addition to these 18 contributed talks, WST 2012, hosts three invited talks by Alexander Krauss, Martin Hofmann, and Fausto Spoto
Euclidean distance geometry and applications
Euclidean distance geometry is the study of Euclidean geometry based on the
concept of distance. This is useful in several applications where the input
data consists of an incomplete set of distances, and the output is a set of
points in Euclidean space that realizes the given distances. We survey some of
the theory of Euclidean distance geometry and some of the most important
applications: molecular conformation, localization of sensor networks and
statics.Comment: 64 pages, 21 figure
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