deterministic bounds
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2021 ◽  
Vol 1 (1) ◽  
pp. 13-20
Author(s):  
Tao Bao ◽  
Mohammed Nabil EL KORSO

The co-centered orthogonal loop and dipole (COLD) array exhibits some interesting properties, which makes it ubiquitous in the context of polarized source localization. In the literature, one can find a plethora of estimation schemes adapted to the COLD array. Nevertheless, their ultimate performance in terms the so-called threshold region of mean square error (MSE), have not been fully investigated. In order to fill this lack, we focus, in this paper, on conditional and unconditional bounds that are tighter than the well known Cramér-Rao Bound (CRB). More precisely, we give some closed form expressions of the McAulay-Hofstetter, the Hammersley-Chapman-Robbins, the McAulaySeidman bounds and the recent Todros-Tabrikian bound, for both the conditional and unconditional observation model. Finally, numerical examples are provided to corroborate the theoretical analysis and to reveal a number of insightful properties.


2020 ◽  
Vol 36 (36) ◽  
pp. 158-168
Author(s):  
Joshua Cape

This note revisits the classical orthogonal Procrustes problem and investigates the norm-dependent geometric behavior underlying Procrustes alignment for subspaces. It presents generic, deterministic bounds quantifying the performance of a specified Procrustes-based choice of subspace alignment. Numerical examples illustrate the theoretical observations and offer additional, empirical findings which are discussed in detail. This note complements recent advances in statistics involving Procrustean matrix perturbation decompositions and eigenvector estimation.


Algorithmica ◽  
2014 ◽  
Vol 72 (3) ◽  
pp. 860-883 ◽  
Author(s):  
Gerth Stølting Brodal ◽  
Spyros Sioutas ◽  
Kostas Tsichlas ◽  
Christos Zaroliagis
Keyword(s):  

2012 ◽  
Vol 268-270 ◽  
pp. 1701-1705
Author(s):  
Ming Chai ◽  
Ping Gu ◽  
Yue Ping Cui

According to the traffic regulating method and the traffic scheduling method of QoS control methods, this paper regulates traffic using the fractal regulator and proposes the arrival curve according to the output envelope of the fractal regulator. In addition, we put forward the service curve based on Enhanced Transmission Selection (ETS). Finally, we drive the deterministic bounds on performance of the self-similar network using the arrival curve and the service curve based on network calculus. These bounds have reference value for QoS guarantee, admission control and network planning.


2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Carlos Hoppen

International audience The analysis of probabilistic algorithms has proved to be very successful for finding asymptotic bounds on parameters of random regular graphs. In this paper, we show that similar ideas may be used to obtain deterministic bounds for one such parameter in the case of regular graphs with large girth. More precisely, we address the problem of finding a large induced forest in a graph $G$, by which we mean an acyclic induced subgraph of $G$ with a lot of vertices. For a fixed integer $r \geq 3$, we obtain new lower bounds on the size of a maximum induced forest in graphs with maximum degree $r$ and large girth. These bounds are derived from the solution of a system of differential equations that arises naturally in the analysis of an iterative probabilistic procedure to generate an induced forest in a graph. Numerical approximations suggest that these bounds improve substantially the best previous bounds. Moreover, they improve previous asymptotic lower bounds on the size of a maximum induced forest in a random regular graph.


Author(s):  
Gerth Stølting Brodal ◽  
Spyros Sioutas ◽  
Kostas Tsichlas ◽  
Christos Zaroliagis
Keyword(s):  

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