Identification of Non-Transversal Bifurcations of Linkages

2020 ◽  
Author(s):  
Andreas Müller ◽  
P. C. López Custodio ◽  
J. S. Dai
Keyword(s):  
Tangent Cone ◽  
Computational Method ◽  
Local Analysis ◽  
Mathematical Framework ◽  
Finite Motion ◽  
Smooth Motion ◽  
Algorithmic Framework ◽  
Definition Of

Abstract The local analysis is an established approach to the study of singularities and mobility of linkages. Key result of such analyses is a local picture of the finite motion through a configuration. This reveals the finite mobility at that point and the tangents to smooth motion curves. It does, however, not immediately allow to distinguish between motion branches that do not intersect transversally (which is a rather uncommon situation that has only recently been discussed in the literature). The mathematical framework for such a local analysis is the kinematic tangent cone. It is shown in this paper that the constructive definition of the kinematic tangent cone already involves all information necessary to separate different motion branches. A computational method is derived by amending the algorithmic framework reported in previous publications.

Identification of Non-Transversal Motion Bifurcations of Linkages

2021 ◽  
Vol 13 (2) ◽  
Author(s):  
Andreas Müller ◽  
P.C. López-Custodio ◽  
J.S. Dai
Keyword(s):  
Tangent Cone ◽  
Computational Method ◽  
Local Analysis ◽  
Mathematical Framework ◽  
Finite Motion ◽  
Smooth Motion ◽  
Transversal Motion ◽  
Algorithmic Framework ◽  
Definition Of

Abstract The local analysis is an established approach to the study of singularities and mobility of linkages. The key result of such analyses is a local picture of the finite motion through a configuration. This reveals the finite mobility at that point and the tangents to smooth motion curves. It does, however, not immediately allow to distinguish between motion branches that do not intersect transversally (which is a rather uncommon situation that has only recently been discussed in the literature). The mathematical framework for such a local analysis is the kinematic tangent cone. It is shown in this paper that the constructive definition of the kinematic tangent cone already involves all information necessary to distinguish different motion branches. A computational method is derived by amending the algorithmic framework reported in previous publications.

Higher-Order Local Analysis of Kinematic Singularities of Lower Pair Linkages

2017 ◽  
Author(s):  
Andreas Müller
Keyword(s):  
Critical Points ◽  
Tangent Cone ◽  
Polynomial System ◽  
Computational Method ◽  
Local Analysis ◽  
Closed Form Expression ◽  
Local Geometry ◽  
Lower Pair ◽  
Kinematic Singularities ◽  
Derivatives Of

Kinematic singularities of linkages are configurations where the differential mobility changes. Constraint singularities are critical points of the constraint mapping defining the loop closure constraints. Configuration space (c-space) singularities are points where the c-space ceases to be a smooth manifold. These singularity types are not identical. C-space singularities are reflected by the c-space geometry. Identifying kinematic singularities amounts to locally analyze the set of critical points. The local geometry of the set of critical points is best approximated by its tangent cone (an algebraic variety). The latter is defined in this paper in a form that allows for its computational determination using the Jacobian minors. An explicit closed form expression for the derivatives of the minors is presented in terms of Lie brackets of joint screws. A computational method is proposed to determine a polynomial system defining the tangent cone. This finally allows for identifying c-space and kinematic singularities.

scholarly journals Identification and inclusion of gender factors in retrospective cohort studies: the GOING-FWD framework

2021 ◽  
Vol 6 (4) ◽  
pp. e005413
Author(s):  
Valeria Raparelli ◽  
Colleen M. Norris ◽  
Uri Bender ◽  
Maria Trinidad Herrero ◽  
Alexandra Kautzky-Willer ◽  
...  
Keyword(s):  
Outcome Measurement ◽  
Meta Analysis ◽  
Synthetic Data ◽  
Well Being ◽  
Pooled Analysis ◽  
Research Network ◽  
Local Analysis ◽  
Related Factors ◽  
Measurement Framework ◽  
Definition Of

Gender refers to the socially constructed roles, behaviours, expressions and identities of girls, women, boys, men and gender diverse people. Gender-related factors are seldom assessed as determinants of health outcomes, despite their powerful contribution. The Gender Outcomes INternational Group: to Further Well-being Development (GOING-FWD) project developed a standard five-step methodology applicable to retrospectively identify gender-related factors and assess their relationship to outcomes across selected cohorts of non-communicable chronic diseases from Austria, Canada, Spain, Sweden. Step 1 (identification of gender-related variables): Based on the gender framework of the Women Health Research Network (ie, identity, role, relations and institutionalised gender), and available literature for a certain disease, an optimal ‘wish-list’ of gender-related variables was created and discussed by experts. Step 2 (definition of outcomes): Data dictionaries were screened for clinical and patient-relevant outcomes, using the International Consortium for Health Outcome Measurement framework. Step 3 (building of feasible final list): a cross-validation between variables per database and the ‘wish-list’ was performed. Step 4 (retrospective data harmonisation): The harmonisation potential of variables was evaluated. Step 5 (definition of data structure and analysis): The following analytic strategies were identified: (1) local analysis of data not transferable followed by a meta-analysis combining study-level estimates; (2) centrally performed federated analysis of data, with the individual-level participant data remaining on local servers; (3) synthesising the data locally and performing a pooled analysis on the synthetic data and (4) central analysis of pooled transferable data. The application of the GOING-FWD multistep approach can help guide investigators to analyse gender and its impact on outcomes in previously collected data.

scholarly journals CONCEPTUAL DESIGN FOR ASSEMBLY IN AEROSPACE INDUSTRY: SENSITIVITY ANALYSIS OF MATHEMATICAL FRAMEWORK AND DESIGN PARAMETERS

2021 ◽  
Vol 1 ◽  
pp. 731-740
Author(s):  
Giovanni Formentini ◽  
Claudio Favi ◽  
Claude Cuiller ◽  
Pierre-Eric Dereux ◽  
Francois Bouissiere ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Conceptual Design ◽  
Design Parameters ◽  
Design For Assembly ◽  
Mathematical Framework ◽  
Commercial Aircraft ◽  
System Architectures ◽  
Complex Engineering ◽  
Aircraft System ◽  
Definition Of

AbstractOne of the most challenging activity in the engineering design process is the definition of a framework (model and parameters) for the characterization of specific processes such as installation and assembly. Aircraft system architectures are complex structures used to understand relation among elements (modules) inside an aircraft and its evaluation is one of the first activity since the conceptual design. The assessment of aircraft architectures, from the assembly perspective, requires parameter identification as well as the definition of the overall analysis framework (i.e., mathematical models, equations).The paper aims at the analysis of a mathematical framework (structure, equations and parameters) developed to assess the fit for assembly performances of aircraft system architectures by the mean of sensitivity analysis (One-Factor-At-Time method). The sensitivity analysis was performed on a complex engineering framework, i.e. the Conceptual Design for Assembly (CDfA) methodology, which is characterized by level, domains and attributes (parameters). A commercial aircraft cabin system was used as a case study to understand the use of different mathematical operators as well as the way to cluster attributes.

scholarly journals The Gender Outcomes International Group: to Further Well-being Development (Going-fwd) Methodology on Identification and Inclusion of Gender Factors in Retrospective Cohort Studies

2020 ◽  
Author(s):  
Valeria Raparelli Raparelli ◽  
Colleen M. Norris ◽  
Uri Bender ◽  
Maria Trinidad Herrero ◽  
Alexandra Kautzky-Willer ◽  
...  
Keyword(s):  
Data Structure ◽  
Meta Analysis ◽  
Synthetic Data ◽  
Well Being ◽  
Pooled Analysis ◽  
Research Network ◽  
Local Analysis ◽  
Related Factors ◽  
Individual Level ◽  
Definition Of

Abstract Background: Gender refers to the socially constructed roles, behaviors, expressions, and identities of girls, women, boys, men, and gender diverse people. It influences self-perception, individual’s actions and interactions, as well as the distribution of power and resources in society. Gender-related factors are seldom assessed as determinants of health outcomes, despite their powerful contribution.Methods: Investigators of the GOING-FWD project developed a standard methodology applicable for observational studies to retrospectively identify gender-related factors to assess their relationship to outcomes and applied this method to selected cohorts of non-communicable chronic diseases from Austria, Canada, Spain, Sweden.Results: The following multistep process was applied. Step 1 (Identification of Gender-related Variables): Based on the gender framework of the Women Health Research Network (i.e. gender identity, role, relations, and institutionalized gender), and available literature for a certain disease, an optimal “wish-list” of gender-related variables/factors was created and discussed by experts. Step 2 (Definition of Outcomes): each of the cohort data dictionaries were screened for clinical and patient relevant outcomes, using the ICHOM framework. Step 3 (Building of Feasible Final List): A cross-validation between gender-related and outcome variables available per database and the “wish-list” was performed. Step 4 (Retrospective Data Harmonization): The harmonization potential of variables was evaluated. Step 5 (Definition of Data Structure and Analysis): Depending on the database data structure, the following analytic strategies were identified: (1) local analysis of data not transferable followed by a meta-analysis combining study-level estimates; (2) centrally performed federated analysis of anonymized data, with the individual-level participant data remaining on local servers; (3) synthesizing the data locally and performing a pooled analysis on the synthetic data; and (4) central analysis of pooled transferable data.Conclusion: The application of the GOING-FWD systematic multistep approach can help guide investigators to analyze gender and its impact on outcomes in previously collected data.

Minimum entropy deconvolution and simplicity: A noniterative algorithm

Geophysics ◽  
1985 ◽  
Vol 50 (3) ◽  
pp. 394-413 ◽  
Author(s):  
Carlos A. Cabrelli
Keyword(s):  
Synthetic Data ◽  
Computational Method ◽  
Minimum Entropy ◽  
Autocorrelation Matrix ◽  
Numerical Tests ◽  
Convolution Model ◽  
Single Input ◽  
Definition Of ◽  
Single Matrix ◽  
New Criterion

Minimum entropy deconvolution (MED) is a technique developed by Wiggins (1978) with the purpose of separating the components of a signal, as the convolution model of a smooth wavelet with a series of impulses. The advantage of this method, as compared with traditional methods, is that it obviates strong hypotheses over the components, which require only the simplicity of the output. The degree of simplicity is measured with the Varimax norm for factor analysis. An iterative algorithm for computation of the filter is derived from this norm, having as an outstanding characteristic its stability in presence of noise. Geometrical analysis of the Varimax norm suggests the definition of a new criterion for simplicity: the D norm. In case of multiple inputs, the D norm is obtained through modification of the kurtosis norm. One of the most outstanding characteristics of the new criterion, by comparison with the Varimax norm, is that a noniterative algorithm for computation of the deconvolution filter can be derived from the D norm. This is significant because the standard MED algorithm frequently requires in each iteration the inversion of an autocorrelation matrix whose order is the length of the filter, while the new algorithm derived from the D norm requires the inversion of a single matrix. On the other hand, results of numerical tests, performed jointly with Graciela A. Canziani, show that the new algorithm produces outputs of greater simplicity than those produced by the traditional MED algorithm. These considerations imply that the D criterion yields a new computational method for minimum entropy deconvolution. A section of numerical examples is included, where the results of an extensive simulation study with synthetic data are analyzed. The numerical computations show in all cases a remarkable improvement resulting from use of the D norm. The properties of stability in the presence of noise are preserved as shown in the examples. In the case of a single input, the relation between the D norm and the spiking filter is analyzed (Appendix B).

An Overview of Positioning and Data Fusion Techniques Applied to Land Vehicle Navigation Systems

2010 ◽  
pp. 219-246 ◽  
Author(s):  
Denis Gingras
Keyword(s):  
Data Fusion ◽  
Mathematical Framework ◽  
Positioning System ◽  
Navigation Systems ◽  
Positioning Systems ◽  
Future Evolution ◽  
Land Vehicle Navigation ◽  
One Step ◽  
Definition Of ◽  
Position Estimate

In this chapter, the authors will review the problem of estimating in real-time the position of a vehicle for use in land navigation systems. After describing the application context and giving a definition of the problem, they will look at the mathematical framework and technologies involved to design positioning systems. The authors will compare the performance of some of the most popular data fusion approaches and provide some insights on their limitations and capabilities. They will then look at the case of robustness of the positioning system when one or some of the sensors are faulty and will describe how the positioning system can be made more robust and adaptive in order to take into account the occurrence of faulty or degraded sensors. Finally, they will go one step further and explore possible architectures for collaborative positioning systems, whereas many vehicles are interacting and exchanging data to improve their own position estimate. The chapter is concluded with some remarks on the future evolution of the field.

Local Analysis of Closed-Loop Linkages: Mobility, Singularities, and Shakiness

2015 ◽  
Author(s):  
Andreas Müller
Keyword(s):  
Tangent Cone ◽  
Local Approximation ◽  
Approximation Order ◽  
Local Analysis ◽  
Space Geometry ◽  
Geometric Entity ◽  
Best Local Approximation ◽  
Kinematic Singularities ◽  
General Configuration

The mobility of a linkage is determined by the constraints imposed on its members. The constraints define the configuration space (c-space) variety as the geometric entity in which the finite mobility of a linkage is encoded. The instantaneous motions are determined by the constraints, rather than by the c-space geometry. Shaky linkages are prominent examples that exhibit a higher instantaneous than finite DOF even in regular configurations. Inextricably connected to the mobility are kinematic singularities that are reflected in a change of the instantaneous DOF. The local analysis of a linkage, aiming at determining the instantaneous and finite mobility in a given configuration, hence needs to consider the c-space geometry as well as the constraint system. A method for the local analysis is presented based on a higher-order local approximation of the c-space adopting the concept of the tangent cone to a variety. The latter is the best local approximation of the c-space in a general configuration. It thus allows for investigating the mobility in regular as well as singular configurations. Therewith the c-space is locally represented as an algebraic variety whose degree is the necessary approximation order. In regular configurations the tangent cone is the tangent space. The method is generally applicable and computationally simple. It allows for a classification of linkages as overconstrained and underconstrained, and to identify singularities.

scholarly journals Defining and Evaluating Microbial Contributions to Metabolite Variation in Microbiome-Metabolome Association Studies

2018 ◽  
Author(s):  
Cecilia Noecker ◽  
Hsuan-Chao Chiu ◽  
Colin P. McNally ◽  
Elhanan Borenstein
Keyword(s):  
Microbial Community ◽  
Predictive Value ◽  
Association Studies ◽  
Ground Truth ◽  
Metabolic Model ◽  
Research Approach ◽  
Mathematical Framework ◽  
Microbial Taxon ◽  
Metabolic Variation ◽  
Definition Of

AbstractCorrelation-based analysis of paired microbiome-metabolome datasets is becoming a widespread research approach, aiming to comprehensively identify microbial drivers of metabolic variation. To date, however, the limitations of this approach have not been comprehensively evaluated. To address this challenge, we introduce a mathematical framework to quantify the contribution of each taxon to metabolite variation based on uptake and secretion fluxes. We additionally use a multi-species metabolic model to simulate simplified gut communities, generating idealized microbiome-metabolome datasets. We then compare observed taxon-metabolite correlations in these datasets to calculated ground-truth taxonomic contribution values. We find that in simulations of both a model 10-species community and of complex human gut microbiota, correlation-based analysis poorly identifies key contributors, with extremely low predictive value despite the idealized setting. We further demonstrate that the predictive value of correlation analysis is strongly influenced by both metabolite and taxon properties, as well as exogenous environmental variation. We finally discuss the practical implications of our findings for interpreting microbiome-metabolome studies.ImportanceIdentifying the key microbial taxa responsible for metabolic differences between microbiomes is an important step towards understanding and manipulating microbiome metabolism. To achieve this goal, researchers commonly conduct microbiome-metabolome association studies, comprehensively measuring both the composition of species and the concentration of metabolites across a set of microbial community samples, and then testing for correlations between microbes and metabolites. Here, we evaluated the utility of this general approach by first developing a rigorous mathematical definition of the contribution of each microbial taxon to metabolite variation, and then examining these contributions in simulated datasets of microbial community metabolism. We found that standard correlation-based analysis of our simulated microbiome-metabolome datasets identifies true contributions with very low predictive value, and that its performance depends strongly on specific properties of both metabolites and microbes, as well as on the surrounding environment. Combined, our findings can guide future interpretation and validation of microbiome-metabolome studies.

scholarly journals Determining Asymptotic Stability and Robustness of Networked Systems

Systems ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 39
Author(s):  
Elias August
Keyword(s):  
Asymptotic Stability ◽  
Equilibrium Points ◽  
Rational Functions ◽  
Computational Method ◽  
Multiple Equilibrium ◽  
Local Analysis ◽  
Stable Equilibrium Point ◽  
Continuous Stirred Tank Reactor ◽  
Novel Approach ◽  
Individual System

This paper is motivated by the notion that coupling systems allows for mitigating the failure of individual ones. We present a novel approach to determining asymptotic stability and robustness of a network consisting of coupled dynamical systems, where individual system dynamics are represented through polynomial or rational functions. The analysis relies on a local analysis; thus, making it computationally implementable. We present an efficient computational method that relies on semidefinite programming. Importantly, for cases where multiple equilibrium points exist, we show how to determine regions around an asymptotically stable equilibrium point that bounds solutions. These regions increase when systems are coupled as we observe when applying the presented analysis framework to a mathematical model of a continuous stirred tank reactor. Importantly, the presented work has implications to other fields as well.

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