Computing stable models: worst-case performance estimates

We propose and study algorithms to compute minimal models, stable models and answer sets of $t$-CNF theories, and normal and disjunctive $t$-programs. We are especially interested in algorithms with non-trivial worst-case performance bounds. The bulk of the paper is concerned with the classes of 2- and 3-CNF theories, and normal and disjunctive 2- and 3-programs, for which we obtain significantly stronger results than those implied by our general considerations. We show that one can find all minimal models of 2-CNF theories and all answer sets of disjunctive 2-programs in time $O(m1\mbox{.}4422\mbox{..}^n)$. Our main results concern computing stable models of normal 3-programs, minimal models of 3-CNF theories and answer sets of disjunctive 3-programs. We design algorithms that run in time $O(m1\mbox{.}6701\mbox{..}^n)$, in the case of the first problem, and in time $O(mn^2 2\mbox{.}2782\mbox{..}^n)$, in the case of the latter two. All these bounds improve by exponential factors the best algorithms known previously. We also obtain closely related upper bounds on the number of minimal models, stable models and answer sets a $t$-CNF theory, a normal $t$-program or a disjunctive $t$-program may have.

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Identifying Model Weakness with Adversarial Examiner

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v34i07.6876 ◽

2020 ◽

Vol 34 (07) ◽

pp. 11998-12006 ◽

Cited By ~ 1

Author(s):

Michelle Shu ◽

Chenxi Liu ◽

Weichao Qiu ◽

Alan Yuille

Keyword(s):

Test Data ◽

Current Model ◽

Autonomous Driving ◽

Worst Case ◽

Average Case ◽

Constructive Feedback ◽

Data Space ◽

Systematic Exploration ◽

Testing Stage ◽

Performance Estimates

Machine learning models are usually evaluated according to the average case performance on the test set. However, this is not always ideal, because in some sensitive domains (e.g. autonomous driving), it is the worst case performance that matters more. In this paper, we are interested in systematic exploration of the input data space to identify the weakness of the model to be evaluated. We propose to use an adversarial examiner in the testing stage. Different from the existing strategy to always give the same (distribution of) test data, the adversarial examiner will dynamically select the next test data to hand out based on the testing history so far, with the goal being to undermine the model's performance. This sequence of test data not only helps us understand the current model, but also serves as constructive feedback to help improve the model in the next iteration. We conduct experiments on ShapeNet object classification. We show that our adversarial examiner can successfully put more emphasis on the weakness of the model, preventing performance estimates from being overly optimistic.

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A Multi-Objective Optimization Model of Health, Safety, and Environmental Risks of Coastal Landfills (A Case Study of the Coastal City of Bandar Abbas)

The Journal of Tolooebehdasht ◽

10.18502/tbj.v20i3.7471 ◽

2021 ◽

Author(s):

Fatemeh Arazm ◽

Seyed Abolghasem Mirhosseini ◽

Mohsen Dehghani ◽

Mahnaz BarkhordariAhmadi

Keyword(s):

Risk Assessment ◽

Environmental Risks ◽

Landfill Site ◽

Multi Objective Optimization ◽

Case Scenario ◽

Worst Case ◽

Health Safety ◽

Multi Objective ◽

Bandar Abbas ◽

Stable Models

Introduction: The increasing development of urban life is one of the fundamental challenges in urban management of waste disposal. Solid municipal waste is one of the major problems of governments and urban planners worldwide, especially in coastal cities. This study aimed to design of an advanced linear planning algorithm for coastal landfills with a focus on safety, health, and environmental risks. Method: This is a qualitative study. Multi-objective optimization presents a mathematical model by evaluating the three risks of health, safety, and environment. First, the data were collected using interviews and qualitative analysis, and then in the second stage, the analysis was presented using model linear planning. Results: In the risk assessment of the landfill site, the presented computational results can be found that stable models provide unfavorable answers compared to definitive models. This is a natural issue; since in stable models, the worst case scenario is considered to achieve the optimal solution, and therefore the resulting answers are always unfavorable compared to the definitive models. Conclusion: By analyzing the risk assessment at the landfill site, the causes of accidents and complications resulting from work in this place include unsafe practices or unsafe and unsanitary conditions. In fact, trying to create and improve health, safety, and environmental conditions of landfills in Bandar Abbas city and the increase in reliability confirmed that these two factors are the secondary causes of accidents. The root causes can be considered as a defect in the management system of the landfill site.

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Mosaic Mapping: A Means of Tiling Images to Shorten Acquisition Speed for Lower - Magnification SEM Images and Wavelength Dispersive Spectrometers (WDS) X-Ray Maps

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100164659 ◽

1996 ◽

Vol 54 ◽

pp. 438-439

Author(s):

J.D. Geller ◽

C.R. Herrington

Keyword(s):

Limiting Factors ◽

X Rays ◽

Angular Range ◽

Acceptance Angle ◽

Sem Images ◽

Worst Case ◽

X Ray ◽

Focusing Distance ◽

Layered Crystals ◽

Working Distance

The minimum magnification for which an image can be acquired is determined by the design and implementation of the electron optical column and the scanning and display electronics. It is also a function of the working distance and, possibly, the accelerating voltage. For secondary and backscattered electron images there are usually no other limiting factors. However, for x-ray maps there are further considerations. The energy-dispersive x-ray spectrometers (EDS) have a much larger solid angle of detection that for WDS. They also do not suffer from Bragg’s Law focusing effects which limit the angular range and focusing distance from the diffracting crystal. In practical terms EDS maps can be acquired at the lowest magnification of the SEM, assuming the collimator does not cutoff the x-ray signal. For WDS the focusing properties of the crystal limits the angular range of acceptance of the incident x-radiation. The range is dependent upon the 2d spacing of the crystal, with the acceptance angle increasing with 2d spacing. The natural line width of the x-ray also plays a role. For the metal layered crystals used to diffract soft x-rays, such as Be - O, the minimum magnification is approximately 100X. In the worst case, for the LEF crystal which diffracts Ti - Zn, ˜1000X is the minimum.

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