scholarly journals THREE SIMPLE HEURISTICS MATHEMATICAL PROOFS ON LASSO THEORY

2020 ◽  
Vol 38 (2) ◽  
pp. 243
Author(s):  
Carlos José dos REIS ◽  
Laerte Dias de CARVALHO ◽  
Lucas Monteiro CHAVES ◽  
Devanil Jaques de SOUZA
Keyword(s):  
Unbiased Estimator ◽  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Tuning Parameter ◽  
Geometrical Approach ◽  
Mathematical Proofs ◽  
Selection Operator ◽  
Simple Heuristics

Three relevant facts about the least absolute shrinkage and selection operator (Lasso) are studied: The estimatives follows piecewise linear curves in relation to tuning parameter, the number of nonzero selected covariates is an unbiased estimator of its degrees of freedom and when the number of covariates p is greater than the numbers of observations n at most n covariates are selected. These results are well known and described in the literature, but with no simple demonstrations. We present, based on a geometrical approach, simple and intuitive heuristics proofs for these results.

Nonlinear Dynamics of One-Way Clutches in Belt-Pulley Systems

2003 ◽  
Author(s):  
Farong Zhu ◽  
Robert G. Parker
Keyword(s):  
Nonlinear Dynamics ◽  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Primary Resonance ◽  
Harmonic Balance Method ◽  
Excitation Amplitude ◽  
Relative Displacement ◽  
Second Primary ◽  
Arc Length ◽  
The One

One-way clutches are frequently used in the serpentine belt accessory drives of automobiles and heavy vehicles. The clutch plays a role similar to a vibration absorber in order to reduce belt/pulley vibration and noise and increase belt life. This paper analyzes a two-pulley system where the driven pulley has a one-way clutch between the pulley and accessory shaft that engages only for positive relative displacement between these components. The belt is modeled with linear springs that transmit torque from the driving pulley to the accessory pulley. The one-way clutch is modeled as a piecewise linear spring with discontinuous stiffness that separates the driven pulley into two degrees of freedom (DOF). The harmonic balance method (HBM) combined with arc-length continuation is employed to illustrate the nonlinear dynamic behavior of the one-way clutch. HBM with arc-length continuation yields the stable and unstable periodic solutions for given parameters. These solutions are examined across a range of excitation frequencies. The results are confirmed by numerical integration and the widely used bifurcation software AUTO. At the first primary resonance, most of the responses are aperiodic, including quasiperiodic and chaotic solutions. At the second primary resonance, the peak bends to the left with classical softening nonlinearity because clutch disengagement decouples the pulley and the accessory over portions of the response period. The dependence on system parameters such as clutch stiffness, excitation amplitude, and inertia ratio between the pulley and accessory is studied to characterize the nonlinear dynamics across a range of conditions.

scholarly journals Gene Selection using a High-Dimensional Regression Model with Microarrays in Cancer Prognostic Studies

2012 ◽  
Vol 11 ◽  
pp. CIN.S9048 ◽  
Author(s):  
Shuhei Kaneko ◽  
Akihiro Hirakawa ◽  
Chikuma Hamada
Keyword(s):  
False Positive ◽  
Cross Validation ◽  
Gene Selection ◽  
Cox Model ◽  
False Positive Rate ◽  
Real Data ◽  
Tuning Parameter ◽  
High Dimensional ◽  
Positive Rate ◽  
Selection Operator

Mining of gene expression data to identify genes associated with patient survival is an ongoing problem in cancer prognostic studies using microarrays in order to use such genes to achieve more accurate prognoses. The least absolute shrinkage and selection operator (lasso) is often used for gene selection and parameter estimation in high-dimensional microarray data. The lasso shrinks some of the coefficients to zero, and the amount of shrinkage is determined by the tuning parameter, often determined by cross validation. The model determined by this cross validation contains many false positives whose coefficients are actually zero. We propose a method for estimating the false positive rate (FPR) for lasso estimates in a high-dimensional Cox model. We performed a simulation study to examine the precision of the FPR estimate by the proposed method. We applied the proposed method to real data and illustrated the identification of false positive genes.

Extracting Articulation Models from CAD Models of Parts With Curved Surfaces

2001 ◽  
Vol 124 (1) ◽  
pp. 106-114 ◽  
Author(s):  
Rajarishi Sinha ◽  
Satyandra K. Gupta ◽  
Christiaan J. J. Paredis ◽  
Pradeep K. Khosla
Keyword(s):  
Contact Mechanics ◽  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Curved Surfaces ◽  
Global Motion ◽  
Intended Behavior ◽  
Cad Models ◽  
Constraint Method ◽  
Motion Behavior ◽  
Algebraic Constraint

In an assembly, degrees of freedom are realized by creating mating features that permit relative motion between parts. In complex assemblies, interactions between individual degrees of freedom may result in a behavior different from the intended behavior. In addition, current methods perform assembly reasoning by approximating curved surfaces as piecewise linear surfaces. Therefore, it is important to be able to reason about assemblies using exact representations of curved surfaces; verify global motion behavior of parts in the assembly; and create motion simulations of the assembly by examination of the geometry and material properties. In this paper, we present a linear algebraic constraint method to automatically construct the space of allowed instantaneous motions of an assembly from the geometry of its constituent parts. Our work builds on previous work on linear contact mechanics and curved surface contact mechanics. We enumerate the conditions under which general curved surfaces can be represented using a finite number of constraints that are linear in the instantaneous velocities. We compose such constraints to build a space of allowed instantaneous velocities for the assembly. The space is then described as a set-theoretic sum of contact-preserving and contact-breaking subspaces. Analysis of each subspace provides feedback to the designer, which we demonstrate through the use of an example assembly—a 4-part mechanism. Finally, the results of the analysis of a 4-bar linkage are compared to those from mechanism theory.

Synthesis of Planar, Shape-Changing Rigid-Body Mechanisms

2006 ◽  
Author(s):  
Brian M. Korte ◽  
Andrew P. Murray ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Shape Change ◽  
Piecewise Linear ◽  
Single Chain ◽  
Open Chain ◽  
Revolute Joints ◽  
Planar Shape ◽  
Rigid Body Displacement ◽  
Planar Linkages

This paper presents a procedure to synthesize planar linkages, composed of rigid links and revolute joints, capable of approximating a shape change defined by a set of curves. These “morphing curves” differ from each other by a combination of rigid-body displacement and shape change. Rigid link geometry is determined through analysis of piecewise linear curves to achieve shape-change approximation, and increasing the number of links improves the approximation. A mechanism is determined through connecting the rigid links into a single chain and adding dyads to eliminate degrees of freedom. The procedure is applied to two open-chain examples.

scholarly journals Towards an improved description of ocean uncertainties: effect of local anamorphic transformations on spatial correlations

2011 ◽  
Vol 8 (5) ◽  
pp. 2147-2195 ◽  
Author(s):  
J.-M. Brankart ◽  
C.-E. Testut ◽  
D. Béal ◽  
M. Doron ◽  
C. Fontana ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Correlation Radius ◽  
Correlation Structure ◽  
General Tendency ◽  
Spatial Correlations ◽  
Parameter Uncertainties ◽  
Large Size ◽  
Observation Network ◽  
Spatial Correlation Structure

Abstract. The objective of this paper is to investigate if the description of ocean uncertainties can be significantly improved by applying a local anamorphic transformation to each model variable, and by making the assumption of joint Gaussianity for the transformed variables, rather than for the original variables. For that purpose, it is first argued that a significant improvement can already be obtained by deriving the local transformations from a simple histogram description of the marginal distributions. Two distinctive advantages of this solution for large size applications are the conciseness and the numerical efficiency of the description. Second, various oceanographic examples are used to evaluate the effect of the resulting piecewise linear local anamorphic transformations on the spatial correlation structure. These examples include (i) stochastic ensemble descriptions of the effect of atmospheric uncertainties on the ocean mixed layer, and of wind uncertainties or parameter uncertainties on the ecosystem, and (ii) non-stochastic ensemble descriptions of forecast uncertainties in current sea ice and ecosystem pre-operational developments. The results indicate that (i) the transformation is accurate enough to faithfully preserve the correlation structure if the joint distribution is already close to Gaussian, and (ii) the transformation has the general tendency of increasing the correlation radius as soon as the spatial dependence between random variables becomes nonlinear, with the important consequence of reducing the number of degrees of freedom in the uncertainties, and thus increasing the benefit that can be expected from a given observation network.

Workspace Analysis of a Three DOF Cable-Driven Mechanism

2009 ◽  
Vol 1 (4) ◽  
Author(s):  
Alireza Alikhani ◽  
Saeed Behzadipour ◽  
S. Ali Sadough Vanini ◽  
Aria Alasty
Keyword(s):  
Degrees Of Freedom ◽  
Large Scale ◽  
Parallel Robot ◽  
External Loading ◽  
Geometrical Shape ◽  
Geometrical Approach ◽  
Workspace Analysis ◽  
Tensile Forces ◽  
Rotational Motions ◽  
Three Degrees Of Freedom

A cable-driven mechanism based on the idea of BetaBot (2005, “A New Cable-Based Parallel Robot With Three Degrees of Freedom,” Multibody Syst. Dyn., 13, pp. 371–383) is analyzed and geometrical description of its workspace boundary is found. In this mechanism, the cable arrangement eliminates the rotational motions leaving the moving platform with three translational motions. The mechanism has potentials for large scale manipulation and robotics in harsh environments. A detailed analysis of the tensionable workspace of the mechanism is presented. The mechanism, in a tensionable position, can develop tensile forces in all cables to maintain its rigidity under arbitrary external loading. A set of conditions on the geometry of the mechanism is proposed for which the tensionable workspace becomes a well defined convex polyhedron. The geometrical shape of the workspace is then described and the tensionability of the mechanism inside the workspace is proved. The proof is quite general and based on a geometrical approach.

Improved Internal Model Control-Proportional-Integral- Derivative Fractional-Order Multiloop Controller Design for Non Integer Order Multivariable Systems

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Tassadit Chekari ◽  
Rachid Mansouri ◽  
Maamar Bettayeb
Keyword(s):  
Fractional Order ◽  
Degrees Of Freedom ◽  
Controller Design ◽  
Mimo Systems ◽  
Design Method ◽  
Internal Model Control ◽  
Tuning Parameter ◽  
Multivariable Systems ◽  
Integer Order ◽  
Model Control

This paper is aimed to propose a multiloop control scheme for fractional order multi-input multi-output (FO-MIMO) systems. It is an extension of the FO-multiloop controller design method developed for integer order multivariable systems to FO-MIMO ones. The interactions among the control loops are considered as disturbances and a two degrees-of-freedom (2DOF) paradigm is used to deal with the process outputs performance and the interactions reduction effect, separately. The proposed controller design method is simple, in relation with the desired closed-loop specifications and a tuning parameter. It presents an interest in controlling complex MIMO systems since fractional order models (FO-models) represent some real processes better than integer order ones and high order systems can be approximated by FO-models. Two examples are considered and compared with other existing methods to evaluate the proposed controller.

scholarly journals Edge-oriented and steerable hyperbolic polaritons in anisotropic van der Waals nanocavities

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Zhigao Dai ◽  
Guangwei Hu ◽  
Guangyuan Si ◽  
Qingdong Ou ◽  
Qing Zhang ◽  
...  
Keyword(s):  
Figure Of Merit ◽  
Degrees Of Freedom ◽  
Optical Axis ◽  
Hexagonal Boron Nitride ◽  
Van Der Waals ◽  
Real Space ◽  
Crystallographic Direction ◽  
Tuning Parameter ◽  
Low Loss ◽  
Plane Anisotropy

AbstractHighly confined and low-loss polaritons are known to propagate isotropically over graphene and hexagonal boron nitride in the plane, leaving limited degrees of freedom in manipulating light at the nanoscale. The emerging family of biaxial van der Waals materials, such as α-MoO3 and V2O5, support exotic polariton propagation, as their auxiliary optical axis is in the plane. Here, exploiting this strong in-plane anisotropy, we report edge-tailored hyperbolic polaritons in patterned α-MoO3 nanocavities via real-space nanoimaging. We find that the angle between the edge orientation and the crystallographic direction significantly affects the optical response, and can serve as a key tuning parameter in tailoring the polaritonic patterns. By shaping α-MoO3 nanocavities with different geometries, we observe edge-oriented and steerable hyperbolic polaritons as well as forbidden zones where the polaritons detour. The lifetime and figure of merit of the hyperbolic polaritons can be regulated by the edge aspect ratio of nanocavity.

Sign in / Sign up

Export Citation Format

Share Document