Lower Bounds on Box Counting

2018 ◽  
pp. 29-37
Author(s):  
Eric Rosenberg
Keyword(s):  
Lower Bounds ◽  
Box Counting

scholarly journals ON- AND OFF-DIAGONAL STURMIAN OPERATORS: DYNAMIC AND SPECTRAL DIMENSION

2012 ◽  
Vol 24 (05) ◽  
pp. 1250011 ◽  
Author(s):  
LAURENT MARIN
Keyword(s):  
Transfer Matrix ◽  
Lower Bounds ◽  
Upper Bound ◽  
Spectral Dimension ◽  
Jacobi Matrices ◽  
Dynamical Exponent ◽  
Box Counting ◽  
Box Counting Dimension

We study two versions of quasicrystal model, both subcases of Jacobi matrices. For the off-diagonal model, we show an upper bound of dynamical exponent and the norm of the transfer matrix. We apply this result to the off-diagonal Fibonacci Hamiltonian and obtain a sub-ballistic bound for coupling large enough. In the diagonal case, we improve previous lower bounds on the fractal box-counting dimension of the spectrum.

Lower Bounds on Box Counting for Complex Networks

2013 ◽  
Vol 14 (04) ◽  
pp. 1350019 ◽  
Author(s):  
ERIC ROSENBERG
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Location Problem ◽  
Facility Location Problem ◽  
Upper And Lower Bounds ◽  
Covering Problem ◽  
Linear Programming Relaxation ◽  
Approximation Methods ◽  
Box Counting ◽  
Effective Approximation

Determining the fractal dimension dB of a complex network requires computing N(s), the minimal number of boxes of size s needed to cover the network. While effective approximation methods for this problem are known, the computation of a lower bound on N(s) has not been studied. We show that a lower bound can be obtained by formulating the covering problem as an uncapacitated facility location problem, and applying dual ascent to the dual of its linear programming relaxation. We illustrate the method on a small example, and provide numerical results on some larger problems. The upper and lower bounds on N(s) can be used to define a linear program which yields upper and lower bounds on dB.

Lower Bounds in Communication Complexity

2007 ◽  
Author(s):  
T. Lee ◽  
A. Shraibman
Keyword(s):  
Lower Bounds ◽  
Communication Complexity

Two Lower Bounds for Shortest Double-Base Number System

2015 ◽  
Vol E98.A (6) ◽  
pp. 1310-1312 ◽  
Author(s):  
Parinya CHALERMSOOK ◽  
Hiroshi IMAI ◽  
Vorapong SUPPAKITPAISARN
Keyword(s):  
Lower Bounds ◽  
Number System ◽  
Base Number ◽  
Double Base

Lower bounds on the dimension of the Rauzy gasket

2020 ◽  
Vol 148 (2) ◽  
pp. 321-327
Author(s):  
Rodolfo Gutiérrez-Romo ◽  
Carlos Matheus
Keyword(s):  
Lower Bounds

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 $K_3$.

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