A lower bound for generalized median based consensus learning using kernel-induced distance functions

2020 ◽  
Vol 140 ◽  
pp. 339-347
Author(s):  
Andreas Nienkötter ◽  
Xiaoyi Jiang
Keyword(s):  
Lower Bound ◽  
Distance Functions ◽  
Generalized Median

scholarly journals On the regular-convexity of Ricci shrinker limit spaces

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Shaosai Huang ◽  
Yu Li ◽  
Bing Wang
Keyword(s):  
Lower Bound ◽  
Ricci Curvature ◽  
Distance Functions ◽  
Regular Part ◽  
Limit Space ◽  
Strongly Convex ◽  
Singular Decomposition ◽  
Original Idea ◽  
Hausdorff Limits

AbstractIn this paper we study the structure of the pointed-Gromov–Hausdorff limits of sequences of Ricci shrinkers. We define a regular-singular decomposition following the work of Cheeger–Colding for manifolds with a uniform Ricci curvature lower bound, and prove that the regular part of any non-collapsing Ricci shrinker limit space is strongly convex, inspired by Colding–Naber’s original idea of parabolic smoothing of the distance functions.

scholarly journals Minimum distance functions of complete intersections

2018 ◽  
Vol 17 (11) ◽  
pp. 1850204 ◽  
Author(s):  
José Martínez-Bernal ◽  
Yuriko Pitones ◽  
Rafael H. Villarreal
Keyword(s):  
Lower Bound ◽  
Complete Intersection ◽  
Polynomial Ring ◽  
Distance Function ◽  
Coding Theory ◽  
Minimum Distance ◽  
Distance Functions ◽  
Complete Intersections ◽  
Dimension One ◽  
Sharp Lower Bound

We study the minimum distance function of a complete intersection graded ideal in a polynomial ring with coefficients in a field. For graded ideals of dimension one, whose initial ideal is a complete intersection, we use the footprint function to give a sharp lower bound for the minimum distance function. Then we show some applications to coding theory.

Assessing flood risk and detecting changes of salt water inflow in a coastal micro-tidal brackish marsh using GIS

2008 ◽  
Vol 37 (3) ◽  
Author(s):  
Jacek Urbański ◽  
Agata Ślimak
Keyword(s):  
Sea Level Rise ◽  
Sea Level ◽  
Flood Risk ◽  
Salt Water ◽  
Brackish Marsh ◽  
Distance Functions ◽  
Water Inflow ◽  
Small Range ◽  
Natural Environments ◽  
Baltic Coast

Assessing flood risk and detecting changes of salt water inflow in a coastal micro-tidal brackish marsh using GISIn order to assess changes in salt water inflow and potential flood risks due to sea level rise in a micro-tidal Beka brackish marsh on the Polish Baltic Coast GIS was used. Such wetlands are important elements of coastal zone natural environments. Creating a geodatabase within a GIS system makes it possible to carry out broad analyses of complex systems, such as coastal wetlands. The results indicate that a 40 cm sea-level rise would considerably increase the frequency of flooding in the investigated area, in part because of the small range of the annual sea level oscillations there. A map of the index of changes in saltwater inflow, created with the help of cost-weighted distance (functions), shows that changes which have occurred along the shore, consisting of filling in the drainage channel outlets, have likely had a significant impact on the vegetation of the area.

The least distance between extremums and minimal period of solutions to autonomous vector differential equations

2019 ◽  
Vol 485 (2) ◽  
pp. 142-144
Author(s):  
A. A. Zevin
Keyword(s):  
Lower Bound ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Lipschitz Constant ◽  
Minimal Period ◽  
Arbitrary Vector ◽  
Vector Norm ◽  
Sharp Lower Bound

Solutions x(t) of the Lipschitz equation x = f(x) with an arbitrary vector norm are considered. It is proved that the sharp lower bound for the distances between successive extremums of xk(t) equals π/L where L is the Lipschitz constant. For non-constant periodic solutions, the lower bound for the periods is 2π/L. These estimates are achieved for norms that are invariant with respect to permutation of the indices.

A Lower Bound for Schur Numbers and Multicolor Ramsey Numbers

10.37236/1188 ◽  
1994 ◽  
Vol 1 (1) ◽  
Author(s):  
Geoffrey Exoo
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Ramsey Numbers

For $k \geq 5$, we establish new lower bounds on the Schur numbers $S(k)$ and on the k-color Ramsey numbers of $K_3$.

On the Crossing Number of $K_{m,n}$

10.37236/1748 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Nagi H. Nahas
Keyword(s):  
Lower Bound ◽  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Crossing Number

The best lower bound known on the crossing number of the complete bipartite graph is : $$cr(K_{m,n}) \geq (1/5)(m)(m-1)\lfloor n/2 \rfloor \lfloor(n-1)/2\rfloor$$ In this paper we prove that: $$cr(K_{m,n}) \geq (1/5)m(m-1)\lfloor n/2 \rfloor \lfloor (n-1)/2 \rfloor + 9.9 \times 10^{-6} m^2n^2$$ for sufficiently large $m$ and $n$.

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