Spectral and threshold analysis of a small rank perturbation of the discrete Laplacian

2021 ◽  
Vol 496 (2) ◽  
pp. 124827
Author(s):  
Zahriddin Muminov ◽  
Shukhrat Alladustov ◽  
Shukhrat Lakaev
Keyword(s):  
Threshold Analysis ◽  
Discrete Laplacian ◽  
Small Rank

scholarly journals Threshold Computation for Spatially Coupled Turbo-Like Codes on the AWGN Channel

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 240
Author(s):  
Muhammad Umar Farooq ◽  
Alexandre Graell i Amat ◽  
Michael Lentmaier
Keyword(s):  
Gaussian Noise ◽  
Belief Propagation ◽  
Additive White Gaussian Noise ◽  
Maximum A Posteriori ◽  
Prediction Methods ◽  
Threshold Analysis ◽  
A Posteriori ◽  
Awgn Channel ◽  
Efficient Prediction ◽  
Binary Erasure Channel

In this paper, we perform a belief propagation (BP) decoding threshold analysis of spatially coupled (SC) turbo-like codes (TCs) (SC-TCs) on the additive white Gaussian noise (AWGN) channel. We review Monte-Carlo density evolution (MC-DE) and efficient prediction methods, which determine the BP thresholds of SC-TCs over the AWGN channel. We demonstrate that instead of performing time-consuming MC-DE computations, the BP threshold of SC-TCs over the AWGN channel can be predicted very efficiently from their binary erasure channel (BEC) thresholds. From threshold results, we conjecture that the similarity of MC-DE and predicted thresholds is related to the threshold saturation capability as well as capacity-approaching maximum a posteriori (MAP) performance of an SC-TC ensemble.

scholarly journals NON-SYMPLECTIC INVOLUTIONS ON MANIFOLDS OF -TYPE

2020 ◽  
pp. 1-25
Author(s):  
CHIARA CAMERE ◽  
ALBERTO CATTANEO ◽  
ANDREA CATTANEO
Keyword(s):  
Moduli Spaces ◽  
Quadratic Forms ◽  
Symplectic Manifolds ◽  
Hilbert Schemes ◽  
Small Rank ◽  
Twisted Sheaves ◽  
Formula Type

We study irreducible holomorphic symplectic manifolds deformation equivalent to Hilbert schemes of points on a $K3$ surface and admitting a non-symplectic involution. We classify the possible discriminant quadratic forms of the invariant and coinvariant lattice for the action of the involution on cohomology and explicitly describe the lattices in the cases where the invariant lattice has small rank. We also give a modular description of all $d$ -dimensional families of manifolds of $K3^{[n]}$ -type with a non-symplectic involution for $d\geqslant 19$ and $n\leqslant 5$ and provide examples arising as moduli spaces of twisted sheaves on a $K3$ surface.

scholarly journals Threshold Analysis and Biodistribution of Fluorescently Labeled Bevacizumab in Human Breast Cancer

2016 ◽  
Vol 77 (3) ◽  
pp. 623-631 ◽  
Author(s):  
Maximilian Koch ◽  
Johannes S. de Jong ◽  
Jürgen Glatz ◽  
Panagiotis Symvoulidis ◽  
Laetitia E. Lamberts ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Human Breast Cancer ◽  
Threshold Analysis ◽  
Human Breast
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