scholarly journals Fast Algorithms for Relational Marginal Polytopes

2021 ◽  
Author(s):  
Yuanhong Wang ◽  
Timothy van Bremen ◽  
Juhua Pu ◽  
Yuyi Wang ◽  
Ondrej Kuzelka
Keyword(s):  
Approximation Scheme ◽  
Fast Algorithms ◽  
Order Model ◽  
Construction Problem ◽  
Past Work ◽  
First Order ◽  
Order Of Magnitude ◽  
Model Counting

We study the problem of constructing the relational marginal polytope (RMP) of a given set of first-order formulas. Past work has shown that the RMP construction problem can be reduced to weighted first-order model counting (WFOMC). However, existing reductions in the literature are intractable in practice, since they typically require an infeasibly large number of calls to a WFOMC oracle. In this paper, we propose an algorithm to construct RMPs using fewer oracle calls. As an application, we also show how to apply this new algorithm to improve an existing approximation scheme for WFOMC. We demonstrate the efficiency of the proposed approaches experimentally, and find that our method provides speed-ups over the baseline for RMP construction of a full order of magnitude.

Lifted Inference with Tree Axioms

2021 ◽  
Author(s):  
Timothy van Bremen ◽  
Ondřej Kuželka
Keyword(s):  
Binary Relation ◽  
Domain Size ◽  
Weighted Sum ◽  
Order Model ◽  
Lifted Inference ◽  
Past Work ◽  
First Order ◽  
Graph Theoretic ◽  
Model Counting ◽  
The Given

We consider the problem of weighted first-order model counting (WFOMC): given a first-order sentence ϕ and domain size n ∈ ℕ, determine the weighted sum of models of ϕ over the domain {1, ..., n}. Past work has shown that any sentence using at most two logical variables admits an algorithm for WFOMC that runs in time polynomial in the given domain size (Van den Broeck 2011; Van den Broeck, Meert, and Darwiche 2014). In this paper, we extend this result to any two-variable sentence ϕ with the addition of a tree axiom, stating that some distinguished binary relation in ϕ forms a tree in the graph-theoretic sense.

scholarly journals Approximate Weighted First-Order Model Counting: Exploiting Fast Approximate Model Counters and Symmetry

2020 ◽  
Author(s):  
Timothy van Bremen ◽  
Ondrej Kuzelka
Keyword(s):  
Probabilistic Models ◽  
Approximate Model ◽  
Probabilistic Logic ◽  
Markov Logic Networks ◽  
Order Model ◽  
Cardinality Constraints ◽  
Markov Logic ◽  
First Order ◽  
Model Counting ◽  
Input Sentence

We study the symmetric weighted first-order model counting task and present ApproxWFOMC, a novel anytime method for efficiently bounding the weighted first-order model count of a sentence given an unweighted first-order model counting oracle. The algorithm has applications to inference in a variety of first-order probabilistic representations, such as Markov logic networks and probabilistic logic programs. Crucially for many applications, no assumptions are made on the form of the input sentence. Instead, the algorithm makes use of the symmetry inherent in the problem by imposing cardinality constraints on the number of possible true groundings of a sentence's literals. Realising the first-order model counting oracle in practice using the approximate hashing-based model counter ApproxMC3, we show how our algorithm is competitive with existing approximate and exact techniques for inference in first-order probabilistic models. We additionally provide PAC guarantees on the accuracy of the bounds generated.

scholarly journals Weighted First-Order Model Counting in the Two-Variable Fragment With Counting Quantifiers

2021 ◽  
Vol 70 ◽  
pp. 1281-1307
Author(s):  
Ondrej Kuzelka
Keyword(s):  
Order Logic ◽  
First Order Logic ◽  
Order Model ◽  
First Order ◽  
Model Counting

It is known due to the work of Van den Broeck, Meert and Darwiche that weighted first-order model counting (WFOMC) in the two-variable fragment of first-order logic can be solved in time polynomial in the number of domain elements. In this paper we extend this result to the two-variable fragment with counting quantifiers.

A first-order model of thermal lensing of laser propagation in the eye and implications for laser safety

2005 ◽  
Author(s):  
Robert J. Thomas ◽  
Rebecca L. Vincelette ◽  
Gavin D. Buffington ◽  
Amber D. Strunk ◽  
Michael A. Edwards ◽  
...  
Keyword(s):  
Thermal Lensing ◽  
Order Model ◽  
Laser Safety ◽  
First Order ◽  
Laser Propagation

Application of two approaches to model chlorine residuals in Severn Trent Water Ltd (STW) distribution systems

1997 ◽  
Vol 36 (5) ◽  
pp. 317-324 ◽  
Author(s):  
M.J. Rodriguez ◽  
J.R. West ◽  
J. Powell ◽  
J.B. Sérodes
Keyword(s):  
Distribution System ◽  
Distribution Systems ◽  
Treatment Plant ◽  
Residual Chlorine ◽  
Ann Model ◽  
Order Model ◽  
First Order ◽  
Chlorine Decay ◽  
Artificial Neural Network Ann ◽  
Key Parameter

Increasingly, those who work in the field of drinking water have demonstrated an interest in developing models for evolution of water quality from the treatment plant to the consumer's tap. To date, most of the modelling efforts have been focused on residual chlorine as a key parameter of quality within distribution systems. This paper presents the application of a conventional approach, the first order model, and the application of an emergent modelling approach, an artificial neural network (ANN) model, to simulate residual chlorine in a Severn Trent Water Ltd (U.K.) distribution system. The application of the first order model depends on the adequate estimation of the chlorine decay coefficient and the travel time within the system. The success of an ANN model depends on the use of representative data about factors which affect chlorine evolution in the system. Results demonstrate that ANN has a promising capacity for learning the dynamics of chlorine decay. The development of an ANN appears to be justifiable for disinfection control purposes, in cases when parameter estimation within the first order model is imprecise or difficult to obtain.

Interpretation of Electron Transfer Spectra of Iridium (IV) and Osmium(IV) Mixed Chloro-Bromo Complexes

1967 ◽  
Vol 22 (6) ◽  
pp. 945-954 ◽  
Author(s):  
Chr. Klixbüll Jørgensen ◽  
W. Preetz
Keyword(s):  
Electron Transfer ◽  
Faraday Effect ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
University Of Virginia ◽  
First Order ◽  
Order Of Magnitude ◽  
Moderate Difference ◽  
The University ◽  
As If

The previous M.O. treatment of unsubstituted hexahalides has been modified, taking the results on Faraday effect obtained at the University of Virginia into account. The absorption spectra previously measured of the complexes (M=Os, Ir) trans-MCl4Br2— and trans-MCl2 Br4— are interpreted by a M.O. treatment for the symmetry D4h as electron transfer transitions, including a first-order relativistic (spin-orbit coupling) correction. The concept of holohedrized symmetry is sufficiently valid to allow a description of MCl5Br— and MClBr5— as if they were tetragonal with centre of inversion and ƒac-(or cis-)MCl3Br3— as if they were cubic. It is shown that the ligand-ligand antibonding effects have the same order of magnitude as the moderate difference in optical electronegativity between Cl- and Br-.

Reduced Order Model of MEMS Sensors Near Natural Frequency

2011 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Jose C. Solis Silva
Keyword(s):  
Natural Frequency ◽  
Nonlinear Response ◽  
Casimir Effect ◽  
Electrostatic Force ◽  
Reduced Order Model ◽  
Mass Detection ◽  
Order Model ◽  
Reduced Order ◽  
First Order ◽  
Electrostatically Actuated

The nonlinear response of an electrostatically actuated cantilever beam microresonator sensor for mass detection is investigated. The excitation is near the natural frequency. A first order fringe correction of the electrostatic force, viscous damping, and Casimir effect are included in the model. The dynamics of the resonator is investigated using the Reduced Order Model (ROM) method, based on Galerkin procedure. Steady-state motions are found. Numerical results for uniform microresonators with mass deposition and without are reported.

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