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 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.

Water Treatment Combined Chlorine (Monochloramine) Degradation using Direct Photolysis and Homogeneous Photocatalysis (UV/H2O2, UV/NaOCl) with a Medium Pressure (MP) Lamp as a Source of UV

2014 ◽  
Vol 12 (2) ◽  
pp. 671-681 ◽  
Author(s):  
Ala Abdessemed ◽  
Kamel E. Djebbar ◽  
Amer S. El-Kalliny ◽  
T. Sehili ◽  
Henk Nugteren ◽  
...  
Keyword(s):  
Oh Radicals ◽  
Order Model ◽  
Direct Photolysis ◽  
First Order ◽  
Medium Pressure ◽  
Pseudo First Order ◽  
Homogeneous Photocatalysis ◽  
Photochemical Systems ◽  
Nitrite Nitrate ◽  
The Given

Abstract The objective of this study is to investigate the use of photochemical systems (photolysis, H2O2/UVMP and NaOCl/UVMP) to deplete monochloramine compound with a medium pressure lamp as an irradiation source (200–600 nm). First, it was found that the direct photolysis treatment was a suitable method to degrade the given compound and that this degradation was greatly enhanced by H2O2/UVMP. This could be attributed to radical •OH produced in great amount by the photolysis of H2O2. However, no big advantages were observed when we used NaOCl/UVMP system. Indeed, this process generated radical •OH (but in feeble amount) and also radical Cl• (to form chloramins) and leading consequently to a less degradation rate comparatively to that obtained with H2O2/UVMP. This could be explained by a competition between the two species: •OH and Cl• for the compound. In addition, kinetics data for the three systems were best represented by a pseudo-first-order model and the photodecomposition of NH2Cl has led to the formation of nitrite, nitrate without forming ammonia.It is essential to mention that •OH radicals produced from H2O2/UVMP and NaOCl/UVMP was detected by a photoluminescence (PL) technic using terephthalic acid (TA) as a probe molecule.

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 Overshoot of D-dot sensor in measurement of electric field

2021 ◽  
Vol 2083 (2) ◽  
pp. 022033
Author(s):  
Jinghai Guo ◽  
Liang Ma ◽  
Yinhui Cheng ◽  
Xutong Wang ◽  
Yifei Liu ◽  
...  
Keyword(s):  
Electric Field ◽  
Equivalent Circuit ◽  
Field Measurement ◽  
Equivalent Circuit Model ◽  
Second Order ◽  
Order Model ◽  
Scanning Method ◽  
First Order ◽  
The Given ◽  
Second Order Model

Abstract This paper analyzes the cause of the overshot of the signal measured by D-dot sensor, and points out that the second-order RLC equivalent circuit model can explain the overshot Taking the asymptotic conical antenna as an example, the inductance L of the second-order model is obtained by using CST simulation and Pspice parameter scanning method. The first-order model and the second-order model are used to calculate the electric field waveform. Under the given conditions, the first-order model is used to obtain the electric field waveform, the waveform overshot is serious, the maximum overshoot reaches 27%, while the second-order model is used to improve the ringing phenomenon, And the maximum overshoot is reduced to 5%.The results show that the second-order model is more accurate than the first-order model and can improve the precision of electric field measurement using D-dot sensor.

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.

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