model equivalence
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Author(s):  
M. N. Nikitenkoч ◽  
M. B. Rabinovich ◽  
M. V. Sviridov

An original method has been developed for estimating formation dip and strike from transient induction LWD data, based on focusing in the time domain. The focusing consists in decomposing the measured signals into a time series and diagonalizing the matrix of focused magnetic field components. We have implemented the method and comprehensively tested it in horizontally-layered media used for LWD data inversion to solve geosteering problems and evaluate the formation resistivity. Estimates of the angles contribute to reliable geosteering when choosing a direction of drilling, as well as when inverting data for a complex earth model. A significant reduction in the resource intensity of inversion and model equivalence is achieved by reducing the number of determined parameters.


Author(s):  
Sander Claeys ◽  
Frederik Geth ◽  
Michael Sankur ◽  
Geert Deconinck

2021 ◽  
Vol 8 (10) ◽  
Author(s):  
Sean T. Vittadello ◽  
Michael P. H. Stumpf

In many scientific and technological contexts, we have only a poor understanding of the structure and details of appropriate mathematical models. We often, therefore, need to compare different models. With available data we can use formal statistical model selection to compare and contrast the ability of different mathematical models to describe such data. There is, however, a lack of rigorous methods to compare different models a priori . Here, we develop and illustrate two such approaches that allow us to compare model structures in a systematic way by representing models as simplicial complexes. Using well-developed concepts from simplicial algebraic topology, we define a distance between models based on their simplicial representations. Employing persistent homology with a flat filtration provides for alternative representations of the models as persistence intervals, which represent model structure, from which the model distances are also obtained. We then expand on this measure of model distance to study the concept of model equivalence to determine the conceptual similarity of models. We apply our methodology for model comparison to demonstrate an equivalence between a positional-information model and a Turing-pattern model from developmental biology, constituting a novel observation for two classes of models that were previously regarded as unrelated.


Author(s):  
Christoph Beierle ◽  
Jonas Haldimann

AbstractConditionals are defeasible rules of the form If A then usually B, and they play a central role in many approaches to nonmonotonic reasoning. Normal forms of conditional knowledge bases consisting of a set of such conditionals are useful to create, process, and compare the knowledge represented by them. In this article, we propose several new normal forms for conditional knowledge bases. Compared to the previously introduced antecedent normal form, the reduced antecedent normal form (RANF) represents conditional knowledge with significantly fewer conditionals by taking nonmonotonic entailments licenced by system P into account. The renaming normal form(ρNF) addresses equivalences among conditional knowledge bases induced by renamings of the underlying signature. Combining the concept of renaming normal form with other normal forms yields the renaming antecedent normal form (ρ ANF) and the renaming reduced antecedent normal form (ρ RANF). For all newly introduced normal forms, we show their key properties regarding, existence, uniqueness, model equivalence, and inferential equivalence, and we develop algorithms transforming every conditional knowledge base into an equivalent knowledge base being in the respective normal form. For the most succinct normal form, the ρ RANF, we present an algorithm KBρra systematically generating knowledge bases over a given signature in ρ RANF. We show that the generated knowledge bases are consistent, pairwise not antecedentwise equivalent, and pairwise not equivalent under signature renaming. Furthermore, the algorithm is complete in the sense that, when taking signature renamings and model equivalence into account, every consistent knowledge base is generated. Observing that normalizing the set of all knowledge bases over a signature Σ to ρ RANF yields exactly the same result as KBρra (Σ), highlights the interrelationship between normal form transformations on the one hand and systematically generating knowledge bases in normal form on the other hand.


Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 392
Author(s):  
Kuan Lu ◽  
Haopeng Zhang ◽  
Kangyu Zhang ◽  
Yulin Jin ◽  
Shibo Zhao ◽  
...  

An invariable order reduction model cannot be obtained by the adaptive proper orthogonal decomposition (POD) method in parametric domain, there exists uniqueness of the model with different conditions. In this paper, the transient POD method based on the minimum error of bifurcation parameter is proposed and the order reduction conditions in the parametric domain are provided. The order reduction model equivalence of optimal sampling length is discussed. The POD method was applied for order reduction of a high-dimensional rotor system supported by sliding bearings in a certain speed range. The effects of speed, initial conditions, sampling length, and mode number on parametric domain order reduction are discussed. The existence of sampling length was verified, and two- and three-degrees-of-freedom (DOF) invariable order reduction models were obtained by proper orthogonal modes (POM) on the basis of optimal sampling length.


2020 ◽  
Vol 9 (3) ◽  
pp. 808-817
Author(s):  
Mareike Augsburger ◽  
Andreas Wenger ◽  
Severin Haug ◽  
Sophia Achab ◽  
Yasser Khazaal ◽  
...  

AbstractBackground and aimsBuying-shopping disorder and its transferability to the online sector is controversial. This study investigates in-store and online shopping patterns by comparing data-based modeling to a diagnostic cut-off approach. Further aims were to test model equivalence for gender and identify socio-demographic risk factors.MethodsIn a representative survey, the Bergen Shopping Addiction Scale (BSAS) was applied, using both an online and in-store version. Latent class analyses were followed by multinomial logistic regression analyses to investigate socio-demographic variables. Measurement invariance across genders was tested with multi-group comparisons.ResultsWith N = 1,012, 3-class solutions provided the best model fit for both in-store and online shopping. Most individuals (76, 86%) were grouped in non-addicted classes, followed by risky (21, 11%) and addicted classes (both 3%). Twenty-eight percent of individuals in the online addicted shopping class remained unidentified using the cut-off. For online shopping, only lower age and education differentiated classes significantly.DiscussionResults indicate a close link between online and in-store shopping, albeit with distinguishing features. The cut-off yielded findings discrepant from class probabilities. That buying-shopping disorder mainly affects younger women of lower educational level must be questioned, given the limited associations identified.ConclusionsIt is important not only to consider different settings of pathological shopping, but also to focus on groups that may not have appeared at risk in previous investigations (e.g., men, older age). The BSAS cut-off warrants further research.


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