Euclidean distance degrees of real algebraic groups

Baaijens, JA Jasmijn; Draisma, Jan

doi:10.1016/j.laa.2014.11.012

Cited by 12 publications

(8 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Some of these methods are: Euclidean distance and Mahalanobis distance [41]. The Euclidean distance treats each variable as equally important in calculating the distance, while Mahalanobis distance, which measures the distance between each observation in a multidimensional cloud of points and the centroid of the cloud [42]. The Euclidean distance between vectors x and y is represented in Equation 1, and the Mahalanobis distance D2 is showed in Equation 2.…”

Section: Hierarchical Cluster Analysis and Non-hierarchical Cluster Amentioning

confidence: 99%

Chemical Characterization of PM2.5 at Rural and Urban Sites around the Metropolitan Area of Huancayo (Central Andes of Peru)

et al. 2019

View full text Add to dashboard Cite

The purpose of this study was to determine PM2.5 mass concentration and the contents of trace elements and water-soluble ions in samples collected inside the Metropolitan area of Huancayo. Four monitoring stations were installed at three urban areas (UNCP, HYO, and CHI) and one rural (IGP). The sampling campaign was carried out from March 2017 to November 2017. The PM2.5 content was determined by gravimetric method, and fifteen trace elements (TE) and seven water-soluble ions were detected by inductively coupled plasma mass spectrometry (ICP–MS), and ion chromatography (IC), respectively. Datasets were assessed by one ANOVA test to detect significant differences among monitoring station. Hierarchical cluster analysis (HCA) and principal component analysis (PCA) were applied for source identification. The mean annual concentration of PM2.5 mass concentrations has ranged (average) from 3.4 to 36.8 µg/m3 (16.6 ± 6.8 µg/m3) for the monitoring stations under study. The annual World Health Organization thresholds and national air quality standards were exceeded. Significant differences (p < 0.05) were observed between most trace elements at urban and rural areas. PCA and HCA illustrated that the most important sources of traces element originated of natural origin (soil re-suspension) and vehicular sources (fuel combustion, abrasion of vehicles tires, wear car components).

show abstract

Section: Hierarchical Cluster Analysis and Non-hierarchical Cluster Amentioning

confidence: 99%

Chemical Characterization of PM2.5 at Rural and Urban Sites around the Metropolitan Area of Huancayo (Central Andes of Peru)

et al. 2019

View full text Add to dashboard Cite

show abstract

“…When X ∩ R n is smooth and compact, the closest point will be a critical point and a solution to the nearest point problem. Results on Euclidean distance degrees have a hypothesis requiring genericity of the data point u [1,2,3,12,14,17,22] or study discriminant loci [13]. Our results allow us to handle situations when the data is not generic.…”

Section: Applications and Examplesmentioning

confidence: 88%

A Morse theoretic approach to non-isolated singularities and applications to optimization

Maxim

Rodriguez

Wang

2020

Preprint

View full text Add to dashboard Cite

Let X be a complex affine variety in C N , and let f : C N → C be a polynomial function whose restriction to X is nonconstant. For g : C N → C a general linear function, we study the limiting behavior of the critical points of the one-parameter family of f t := f − tg as t → 0. Our main result gives an expression of this limit in terms of critical sets of the restrictions of g to the singular strata of (X, f ). We apply this result in the context of optimization problems. For example, we consider nearest point problems (e.g., Euclidean distance degrees) for affine varieties and a possibly nongeneric data point.

show abstract

“…In order to improve the assessment accuracy, the generalized weighted distance (i.e. Euclidean distance) in fuzzy mathematics was adopted to represent the difference degree between reference sequence and comparison sequence .…”

Section: Analysis Model Of Influencing Factors Of Vehicle Dpf Composimentioning

confidence: 99%

Comprehensive analysis on influencing factors of composite regeneration performance of a diesel particulate filter

Zuo

Zhang

Jiaqiang

et al. 2015

Env Prog and Sustain Energy

View full text Add to dashboard Cite

In order to effectively improve the composite regeneration performance of the diesel particulate filter in vehicle, a fuzzy gray correlation analysis model based on the composite regeneration influencing factors of diesel particulate filter was established using the cosine value of fuzzy membership and Euclidean distance formula. And, on the basis of experimental data from three‐dimensional computational fluid dynamics simulation, the fuzzy gray correlation analysis on important degree of characteristic indexes, which has influence on the composite regeneration performance of diesel particulate filter, was conducted. Moreover, the method of Lagrange function was used to solve the fuzzy gray affiliate degree based on the results of this fuzzy gray correlation analysis. The effectiveness indexes of overall performance of the diesel particulate filter composite regeneration time, regeneration peak temperature and regeneration efficiency were also obtained. The results showed that the amount of ceria‐based additive had the greatest influence on the regeneration time among all the characteristic performance indexes of diesel particulate filter composite regeneration. Similarly, it could be concluded that the exhaust oxygen concentration and exhaust temperature respectively had the greatest influence on the regeneration peak temperature and regeneration efficiency. In addition, the regeneration time had the greatest influence on the overall performance of diesel particulate filter composite regeneration while the regeneration efficiency took the second place and the influence of the regeneration peak temperature was the minimum. The results of this article showed theoretical significance and reference value for optimization analysis and control of diesel particulate filter composite regeneration process. © 2015 American Institute of Chemical Engineers Environ Prog, 35: 882–890, 2016

show abstract

Euclidean distance degrees of real algebraic groups

Cited by 12 publications

References 7 publications

Chemical Characterization of PM2.5 at Rural and Urban Sites around the Metropolitan Area of Huancayo (Central Andes of Peru)

Chemical Characterization of PM2.5 at Rural and Urban Sites around the Metropolitan Area of Huancayo (Central Andes of Peru)

A Morse theoretic approach to non-isolated singularities and applications to optimization

Comprehensive analysis on influencing factors of composite regeneration performance of a diesel particulate filter

Contact Info

Product

Resources

About