Fast Hankel tensor-vector product and its application to exponential data fitting

2015 ◽  
Vol 22 (5) ◽  
pp. 814-832 ◽  
Author(s):  
Weiyang Ding ◽  
Liqun Qi ◽  
Yimin Wei
Keyword(s):  
Data Fitting ◽  
Vector Product ◽  
Hankel Tensor

An Initial Design for an Extended Vector Product Format Prototype for Modeling and Simulation.

1997 ◽  
Author(s):  
Kevin Shaw ◽  
H. V. Miller ◽  
Barbara Ray ◽  
Robert Broome ◽  
Todd Lovitt
Keyword(s):  
Modeling And Simulation ◽  
Vector Product ◽  
Initial Design

scholarly journals Depth-Sensing Indentation as a Micro- and Nanomechanical Approach to Characterisation of Mechanical Properties of Soft, Biological, and Biomimetic Materials

Nanomaterials ◽  
2019 ◽  
Vol 10 (1) ◽  
pp. 15 ◽  
Author(s):  
Nikolay V. Perepelkin ◽  
Feodor M. Borodich ◽  
Alexander E. Kovalev ◽  
Stanislav N. Gorb
Keyword(s):  
Review Paper ◽  
Soft Materials ◽  
Data Fitting ◽  
Depth Sensing ◽  
Adhesive Properties ◽  
Distinctive Features ◽  
Experimental Part ◽  
Properties Of Materials ◽  
The Mathematical Model ◽  
Non Destructive

Classical methods of material testing become extremely complicated or impossible at micro-/nanoscale. At the same time, depth-sensing indentation (DSI) can be applied without much change at various length scales. However, interpretation of the DSI data needs to be done carefully, as length-scale dependent effects, such as adhesion, should be taken into account. This review paper is focused on different DSI approaches and factors that can lead to erroneous results, if conventional DSI methods are used for micro-/nanomechanical testing, or testing soft materials. We also review our recent advances in the development of a method that intrinsically takes adhesion effects in DSI into account: the Borodich–Galanov (BG) method, and its extended variant (eBG). The BG/eBG methods can be considered a framework made of the experimental part (DSI by means of spherical indenters), and the data processing part (data fitting based on the mathematical model of the experiment), with such distinctive features as intrinsic model-based account of adhesion, the ability to simultaneously estimate elastic and adhesive properties of materials, and non-destructive nature.

scholarly journals Experimental Analysis of Driver Visual Characteristics in Urban Tunnels

2021 ◽  
Vol 11 (9) ◽  
pp. 4274
Author(s):  
Song Fang ◽  
Jianxiao Ma
Keyword(s):  
Traffic Safety ◽  
Clustering Algorithm ◽  
Pupil Diameter ◽  
Data Fitting ◽  
Eye Tracker ◽  
Tunnel Length ◽  
Point Distribution ◽  
Change Rate ◽  
Visual Characteristics ◽  
Diameter Change

Through an urban tunnel-driving experiment, this paper studies the changing trend of drivers’ visual characteristics in tunnels. A Tobii Pro Glasses 2 wearable eye tracker was used to measure pupil diameter, scanning time, and fixation point distribution of the driver during driving. A two-step clustering algorithm and the data-fitting method were used to analyze the experimental data. The results show that the univariate clustering analysis of the pupil diameter change rate of drivers has poor discrimination because the pupil diameter change rate of drivers in the process of “dark adaptation” is larger, while the pupil diameter change rate of drivers in the process of “bright adaptation” is relatively smooth. The univariate and bivariate clustering results of drivers’ pupil diameters were all placed into three categories, with reasonable distribution and suitable differentiation. The clustering results accurately corresponded to different locations of the tunnel. The clustering method proposed in this paper can identify similar behaviors of drivers at different locations in the transition section at the tunnel entrance, the inner section, and the outer area of the tunnel. Through data-fitting of drivers’ visual characteristic parameters in different tunnels, it was found that a short tunnel, with a length of less than 1 km, has little influence on visual characteristics when the maximum pupil diameter is small, and the percentage of saccades is relatively low. An urban tunnel with a length between 1 and 2 km has a significant influence on visual characteristics. In this range, with the increase in tunnel length, the maximum pupil diameter increases significantly, and the percentage of saccades increases rapidly. When the tunnel length exceeds 2 km, the maximum pupil diameter does not continue to increase. The longer the urban tunnel, the more discrete the distribution of drivers’ gaze points. The research results should provide a scientific basis for the design of urban tunnel traffic safety facilities and traffic organization.

scholarly journals On the Accuracy of the Sine Power Lomax Model for Data Fitting

Modelling ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 78-104
Author(s):  
Vasili B. V. Nagarjuna ◽  
R. Vishnu Vardhan ◽  
Christophe Chesneau
Keyword(s):  
Statistical Model ◽  
Simulation Study ◽  
Statistical Models ◽  
Goodness Of Fit ◽  
Data Fitting ◽  
Applied Science ◽  
Survival Distribution ◽  
Lomax Distribution ◽  
Model Based

Every day, new data must be analysed as well as possible in all areas of applied science, which requires the development of attractive statistical models, that is to say adapted to the context, easy to use and efficient. In this article, we innovate in this direction by proposing a new statistical model based on the functionalities of the sinusoidal transformation and power Lomax distribution. We thus introduce a new three-parameter survival distribution called sine power Lomax distribution. In a first approach, we present it theoretically and provide some of its significant properties. Then the practicality, utility and flexibility of the sine power Lomax model are demonstrated through a comprehensive simulation study, and the analysis of nine real datasets mainly from medicine and engineering. Based on relevant goodness of fit criteria, it is shown that the sine power Lomax model has a better fit to some of the existing Lomax-like distributions.

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