A New Approach to the Upper Bound on the Average Distance from the Fermat-Weber Center of a Convex Body

2013 ◽  
pp. 250-259
Author(s):  
Xuehou Tan ◽  
Bo Jiang
Keyword(s):  
Convex Body ◽  
Upper Bound ◽  
Average Distance ◽  
New Approach

scholarly journals On the relative distances of six points in a plane convex body

2005 ◽  
Vol 42 (3) ◽  
pp. 253-264
Author(s):  
Károly Böröczky ◽  
Zsolt Lángi
Keyword(s):  
Convex Body ◽  
Upper Bound ◽  
Euclidean Distance ◽  
Euclidean Plane ◽  
Relative Distance ◽  
Plane Convex ◽  
Euclidean Length ◽  
Plane Convex Body

Let C be a convex body in the Euclidean plane. By the relative distance of points p and q we mean the ratio of the Euclidean distance of p and q to the half of the Euclidean length of a longest chord of C parallel to pq. In this note we find the least upper bound of the minimum pairwise relative distance of six points in a plane convex body.

ON THE GAUSSIAN CURVATURE OF MAXIMAL SURFACES AND THE CALABI–BERNSTEIN THEOREM

2001 ◽  
Vol 33 (4) ◽  
pp. 454-458 ◽  
Author(s):  
LUIS J. ALÍAS ◽  
BENNETT PALMER
Keyword(s):  
Minkowski Space ◽  
Upper Bound ◽  
Gaussian Curvature ◽  
Total Curvature ◽  
Local Geometry ◽  
Maximal Surface ◽  
Bernstein Theorem ◽  
New Approach ◽  
Maximal Surfaces

In this paper, a new approach to the Calabi–Bernstein theorem on maximal surfaces in the Lorentz– Minkowski space L3 is introduced. The approach is based on an upper bound for the total curvature of geodesic discs in a maximal surface in L3, involving the local geometry of the surface and its hyperbolic image. As an application of this, a new proof of the Calabi–Bernstein theorem is provided.

On Oriented Embedding of the Binary Tree into the Hypercube

1994 ◽  
Vol 3 (1) ◽  
pp. 27-38 ◽  
Author(s):  
Sergej L. Bezrukov
Keyword(s):  
Upper Bound ◽  
Binary Tree ◽  
New Approach

We consider the oriented binary tree and the oriented hypercube. The tree edges are oriented from the root to the leaves, while the orientation of the cube edges is induced by the direction from 0 to 1 in the coordinatewise form. The problem is to embed such a tree with l levels into the oriented n-cube as an oriented subgraph, for minimal possible n. A new approach to such problems is presented, which improves the known upper bound n/l ≤ 3/2 given by Havel [1] to n/l ≤ 4/3 + o(1) as l → ∞.

Tight Upper Bound for Accelerating Reconfiguration of VLSI Arrays

2015 ◽  
Vol 24 (07) ◽  
pp. 1550099 ◽  
Author(s):  
Jigang Wu ◽  
Xiaogang Han
Keyword(s):  
Upper Bound ◽  
Large Scale ◽  
Very Large Scale Integration ◽  
New Approach ◽  
Large Target ◽  
Large Scale Integration ◽  
Simulation Results ◽  
Scale Integration ◽  
Target Array ◽  
Vlsi Array

Reconfiguring a very large scale integration (VLSI) array with faults is to construct a maximum logical sub-array (target array) without faults. A large target array implies a good harvest of the corresponding reconfiguration algorithm. Thus, a tight upper bound of the harvest can be directly used to evaluate the performance of the reconfiguration algorithm. This paper presents a new approach to calculate the upper bound of the harvest for the VLSI arrays with clustered faults. The latest upper bound is successfully reduced and the proposed technique to calculate the upper bound is bound into a reconfiguration algorithm cited in this paper. Simulation results show that the upper bound is reduced up to 20% on 256 × 256 array with clustered faults, and the corresponding reconfiguration process is significantly accelerated over 30%, without loss of harvest.

ON FINITENESS OF VASSILIEV INVARIANTS AND A PROOF OF THE LIN-WANG CONJECTURE VIA BRAIDING POLYNOMIALS

2001 ◽  
Vol 10 (05) ◽  
pp. 769-780 ◽  
Author(s):  
A. Stoimenow
Keyword(s):  
Upper Bound ◽  
Special Class ◽  
Crossing Number ◽  
New Approach ◽  
Vassiliev Invariants ◽  
A Value ◽  
Vassiliev Invariant

Using the new approach of braiding sequences we give a proof of the Lin-Wing conjecture, stating that a Vassiliev invariant ν of degree k has a value Oν (c(K)k) on a knot K, where c(K) is the crossing number of K and Oν depends on ν only. We extend our method to give a quadratic upper bound in k for the crossing number of alternating/positive knots, the values on which suffice to determine uniquely a Vassiliev invariant of degree k. This also makes orientation and mutation sensitivity of Vassiliev invariants decidable by testing them on alternating/positive knots/mutants only. We give an exponential upper bound for the number of Vassiliev invariants on a special class of closed braids.

scholarly journals Matrix Liberation Process II: Relation to Orbital Free Entropy

2020 ◽  
pp. 1-49
Author(s):  
Yoshimichi Ueda
Keyword(s):  
Mutual Information ◽  
Upper Bound ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Rate Function ◽  
New Approach ◽  
Free Entropy ◽  
The Matrix ◽  
Orbital Free ◽  
Definition Of

Abstract We investigate the concept of orbital free entropy from the viewpoint of the matrix liberation process. We will show that many basic questions around the definition of orbital free entropy are reduced to the question of full large deviation principle for the matrix liberation process. We will also obtain a large deviation upper bound for a certain family of random matrices that is essential to define the orbital free entropy. The resulting rate function is made up into a new approach to free mutual information.

Improved Understanding of Stent Malapposition Using Virtual Bench Testing

2011 ◽  
Vol 6 (2) ◽  
pp. 106 ◽  
Author(s):  
Peter Mortier ◽  
Heleen MM van Beusekom ◽  
Matthieu De Beule ◽  
Ilona Krabbendam-Peters ◽  
Benjamin Van Der Smissen ◽  
...  
Keyword(s):  
Imaging Techniques ◽  
Average Distance ◽  
Three Dimensional ◽  
Proximal Part ◽  
New Approach ◽  
Incomplete Stent Apposition ◽  
Bifurcation Stenting ◽  
Silicone Model ◽  
Bench Testing

Intravascular imaging techniques such as optical coherence tomography (OCT) and intravascular ultrasound (IVUS) are often used to assess strut apposition, but only provide limited insight into the three-dimensional appositioning behaviour of stents. Recently, a new approach has been introduced to study the phenomenon of incomplete stent apposition (ISA) based on finite element simulations. In this study, we employed this virtual strut apposition assessment technique in the setting of coronary bifurcation stenting and compared simulated strut–artery distances of two stent designs with actual measurements based on OCT imaging using a silicone model. Stenting of the main branch leads to malapposed struts in the proximal part and the average strut–artery distance in that region for the Integrity stent is 126 μm based on the simulation and 117±14 μm based on the OCT analysis. For the Multi-Link 8 stent, this average distance is 150 μm and 174±7 µm for the simulation and thein vitroOCT measurements respectively. In conclusion, the virtual assessment of strut appositioning results in similar strut–artery distances when compared with measurements based on OCT-visualisedin vitrostent deployments and could be used to optimise devices and procedures.

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