scholarly journals Estimating the Reach of a Manifold via its Convexity Defect Function

2021 ◽  
Author(s):  
Clément Berenfeld ◽  
John Harvey ◽  
Marc Hoffmann ◽  
Krishnan Shankar
Keyword(s):  
Lower Bounds ◽  
Manifold Learning ◽  
Point Clouds ◽  
Expected Loss ◽  
Logarithmic Factor ◽  
Stability Properties ◽  
Defect Function ◽  
Geometric Inference ◽  
The Stability ◽  
Minimax Rate

AbstractThe reach of a submanifold is a crucial regularity parameter for manifold learning and geometric inference from point clouds. This paper relates the reach of a submanifold to its convexity defect function. Using the stability properties of convexity defect functions, along with some new bounds and the recent submanifold estimator of Aamari and Levrard (Ann. Statist. 47(1), 177–204 (2019)), an estimator for the reach is given. A uniform expected loss bound over a $${\mathscr {C}}^k$$ C k model is found. Lower bounds for the minimax rate for estimating the reach over these models are also provided. The estimator almost achieves these rates in the $${\mathscr {C}}^3$$ C 3 and $${\mathscr {C}}^4$$ C 4 cases, with a gap given by a logarithmic factor.

scholarly journals Velocity and acceleration level inverse kinematic calculation alternatives for redundant manipulators

Meccanica ◽  
2021 ◽  
Author(s):  
Dóra Patkó ◽  
Ambrus Zelei
Keyword(s):  
Degrees Of Freedom ◽  
Direct Method ◽  
Tracking Error ◽  
Inverse Kinematic ◽  
Linear Feedback ◽  
Joint Position ◽  
Stability Properties ◽  
Acceleration Level ◽  
Error Elimination ◽  
The Stability

AbstractFor both non-redundant and redundant systems, the inverse kinematics (IK) calculation is a fundamental step in the control algorithm of fully actuated serial manipulators. The tool-center-point (TCP) position is given and the joint coordinates are determined by the IK. Depending on the task, robotic manipulators can be kinematically redundant. That is when the desired task possesses lower dimensions than the degrees-of-freedom of a redundant manipulator. The IK calculation can be implemented numerically in several alternative ways not only in case of the redundant but also in the non-redundant case. We study the stability properties and the feasibility of a tracking error feedback and a direct tracking error elimination approach of the numerical implementation of IK calculation both on velocity and acceleration levels. The feedback approach expresses the joint position increment stepwise based on the local velocity or acceleration of the desired TCP trajectory and linear feedback terms. In the direct error elimination concept, the increment of the joint position is directly given by the approximate error between the desired and the realized TCP position, by assuming constant TCP velocity or acceleration. We investigate the possibility of the implementation of the direct method on acceleration level. The investigated IK methods are unified in a framework that utilizes the idea of the auxiliary input. Our closed form results and numerical case study examples show the stability properties, benefits and disadvantages of the assessed IK implementations.

scholarly journals Local compactness in approach spaces II

2003 ◽  
Vol 2003 (2) ◽  
pp. 109-117
Author(s):  
R. Lowen ◽  
C. Verbeeck
Keyword(s):  
Stability Properties ◽  
Local Compactness ◽  
The Stability ◽  
Approach Spaces

This paper studies the stability properties of the concepts of local compactness introduced by the authors in 1998. We show that all of these concepts are stable for contractive, expansive images and for products.

On the stability properties of a third order system

1968 ◽  
Vol 78 (1) ◽  
pp. 91-103 ◽  
Author(s):  
G. P. Szegö ◽  
C. Olech ◽  
A. Cellina
Keyword(s):  
Order System ◽  
Third Order ◽  
Stability Properties ◽  
The Stability

On the Stability Properties of a Periodically Forced, Time-Varying Mass System

2009 ◽  
Author(s):  
W. T. van Horssen ◽  
O. V. Pischanskyy ◽  
J. L. A. Dubbeldam
Keyword(s):  
Periodic Solutions ◽  
Forced Vibrations ◽  
Time Varying ◽  
Mass System ◽  
Single Degree Of Freedom ◽  
Stability Properties ◽  
Single Degree ◽  
Existence Of Periodic Solutions ◽  
The Stability ◽  
Varying Mass

In this paper the forced vibrations of a linear, single degree of freedom oscillator (sdofo) with a time-varying mass will be studied. The forced vibrations are due to small masses which are periodically hitting and leaving the oscillator with different velocities. Since these small masses stay for some time on the oscillator surface the effective mass of the oscillator will periodically vary in time. Not only solutions of the oscillator equation will be constructed, but also the stability properties, and the existence of periodic solutions will be discussed.

scholarly journals Dispersing Hash Functions

2000 ◽  
Vol 7 (36) ◽  
Author(s):  
Rasmus Pagh
Keyword(s):  
Lower Bounds ◽  
Random Function ◽  
Hash Functions ◽  
Expected Value ◽  
Independent Interest ◽  
Upper And Lower Bounds ◽  
Related Issue ◽  
Logarithmic Factor

A new hashing primitive is introduced: dispersing hash functions. A family<br />of hash functions F is dispersing if, for any set S of a certain size and random<br />h in F, the expected value of |S|−|h[S]| is not much larger than the expectancy<br />if h had been chosen at random from the set of all functions.<br />We give tight, up to a logarithmic factor, upper and lower bounds on the<br />size of dispersing families. Such families previously studied, for example <br />universal families, are significantly larger than the smallest dispersing families,<br />making them less suitable for derandomization. We present several applications<br /> of dispersing families to derandomization (fast element distinctness, set<br />inclusion, and static dictionary initialization). Also, a tight relationship <br />between dispersing families and extractors, which may be of independent interest,<br />is exhibited.<br />We also investigate the related issue of program size for hash functions<br />which are nearly perfect. In particular, we exhibit a dramatic increase in<br />program size for hash functions more dispersing than a random function.

scholarly journals Comparison of the Calculations of the Stability Properties of a Specific Stellarator Equilibrium with Different MHD Stability Codes

1996 ◽  
Vol 128 (1) ◽  
pp. 43-57 ◽  
Author(s):  
Y. Nakamura ◽  
T. Matsumoto ◽  
M. Wakatani ◽  
S.A. Galkin ◽  
V.V. Drozdov ◽  
...  
Keyword(s):  
Stability Properties ◽  
Mhd Stability ◽  
The Stability
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